Talk:Riemann hypothesis

3060:: SDNOTDEF does not mean "say something extremely vague in an attempt to avoid saying anything about the topic of the article", it means "aim for understandability and conciseness in explaining what the article is about rather than aiming for a pedantic precise definition". What one needs is something indicating that this is about the locations of the zeros of the zeta function. The status quo, "Conjecture in mathematics linked to the distribution of prime numbers" is more informative, but still doesn't really pinpoint what this is about (the connection to prime numbers is pretty indirect), and is also too long (69 characters when the target length is 40). 3685:, the author seems to have lots of working papers claiming stuff that would be groundbreaking if true (including an alleged proof of the Riemann Hypothesis, and an alleged proof of there being a finite amount of prime numbers). What do you think is going on? I would assume that papers that groundbreaking would be peer reviewed and picked up by major journals, very quickly. Do you think it’s likely that he hasn’t been noticed, that his papers were all disproven but not retracted for some reason, that all his papers were complete bs, or that his papers are waiting to be peer reviewed? 2235:

going the wrong direction, taking a problem that might be decidable somehow (Riemann) and reducing it to a problem that we know is undecidable (termination of even certain simple concrete tag systems). It doesn't help us resolve Riemann because tag systems in general aren't an easy way to solve things, and it doesn't prove hardness of anything because for that you need to translate in the other direction from the known-hard to the unknown. So there is no hope that this kind of translation can be useful as a general solving-problem approach. —

316: 306: 278: 245: 773:, who politely reports that it is not a good book). The report on du Sautoy's book states that it is "not sufficiently accurate and complete". The report on Rockmore's book is not good either (also from Heath-Brown). Finally Derbyshire (who is credited with only 3 reviewed works on MathSciNet!) has the worst review ("While some chapters are not too bad, most seem to miss their mark" "I am not sure the author ever answers the question of why the Riemann hypothesis is important.") 2020:"OED says: Some traditionalists maintain that none can only take a singular verb (as in none of them is coming tonight rather than none of them are coming tonight). However, none is descended from Old English nan meaning ‘not one’, and has been used for around a thousand years with either a singular or a plural verb, depending on the context and the emphasis needed." The answer seems to depend on the source, and there is no definitive right or wrong answer.-- 463: 623:

should be expected to learn those stuff on the way. and though putting the note that Li is referrign to the logarithmic integral function could be put a little early its not all that big of a deal as the logarithmic integral function is already extremely closely tied to the riemann zeta function so its really easy for many people to assume its the logarithmic integral function and not the polylogarithmic one.

416: 577:. Thus, being a relative novice and not knowing which one is referred to (although I can guess), I can't even edit in a link here. Please have some perspective and put yourselves in the situation of someone less well educated, but still keen to learn. If you don't, I will suspect that you are more interested in showing off your expertise than in spreading knowledge. Sorry. 236: 2879:

neglected to mention where and how the proof was wrong. Dozens of “experts” on the RH, approached directly by email, have, with few exceptions, not deigned to reply; and if they did, would not offer an opinion on the correctness of proof, nor point out any fatal error. Other academic mathematicians usually could not even be drawn to read the paper.

382: 2145:, I would like to disagree that the statement is entirely vacuous, and ask for suggestions to improve it. Yes, I agree that since Tag systems are computationally universal, it holds that there would theoretically exist a system which could prove or disprove the Riemann Hypothesis. However, the importance of the statement, is that such a system 292: 2872: 3734:

does the same, and some cranks who never published anything have their complete works on it (what ArXiv does when they eventually realize a paper is bullshit, is to reclassify it as « General Mathematics » - or GM). Of course the Ramanujan J. is a fairly good journal, but cranks have been able in the

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So, does that mean the RH could actually end up being somewhat ambiguous? (I’m thinking, what if it turns out that 1. there are values away from the critical line that _could_ be zeroes, 2. it is possible to show that no algorithm can prove that any of these values is _actually_ zero rather than just

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The committee invited more than 1,200 mathematicians to participate in an open review wherein the referees had to openly reveal their names and institutional affiliations so that everything was transparent to all other experts and nothing could be done anonymously. However, of the 1000 plus invitees,

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Dr Easwaran, who works at Sreenidhi Institute of Science and Technology (SNIST) Hyderabad placed his claims on the internet five years ago. In 2020, after it was downloaded a thousand times, an expert committee consisting of eight mathematicians and theoretical physicists was constituted to look into

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before it was obvious it is log_e. Now, it is not, AT ALL. "As for ISO, pfeh. Nobody follows ISO." Russia, France, et cetera follows ISO. It does not matter anyway, since wikipedia MUST follow ISO. lg is 10 base, log is 2 base. Full stop. "follow number theory conventions" "mathematicians use log for

966:

Sorry if this is well know, but looking at the patterns in 3d (hard to view 4D) of the values of non-prime numbers, it seems like one could simply look at the data around the chosen point to follow it down to 1/2. I guess a proof is (a, all 'fingers' lead down to 1/2 eventually and we know that their

740:

Does it really make sense to break out "Popular expositions" as a separate subsection of the references section? Also, I am puzzled why some things were included and not others. The selection seems rather arbitrary in my opinion, and not really connected with any reliable metric of "popularness" of

3036:

No. You are making a confusion. The current shortdesc doesn’t attempt in any way to define the article. It just attempts to provide something more than a totally useless information on it - which is what your version provides. It is of no help whatsoever to describe as a « mathematical conjecture »

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Perhaps I can elaborate why I think this is irrelevant here, though. I think the universality of tag systems, proved by Minsky in 1961, is worth knowing, but after that point the main use of tag systems is to prove other things universal or undecidable. When you reduce Riemann to tag systems, you're

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Huh? (BTW I saw your edit on my watchlist, but changing a comment to add a ping after-the-fact doesn't work.) By now it's clearer that there was no proof. We already mention this, very briefly and with appropriate skepticism, in our biography of Atiyah. I don't think it rises to the level of needing

3265:

Right! Missed the exception, and in my head I'm often very sloppy up to asymptotic density 0 exceptions. (I am certainly not a real number theorist.) I guess that it would still possibly be due to include in the article something about consequences of the RH for typical prime gaps, but it is not

2882:

All of the above seem united by their utter, if usually unspoken, disbelief that an amateur could prove the Riemann Hypothesis. So, well into the third year after his original paper was uploaded, Kumar Eswaran has still to receive a professional mathematical appraisal of his proof. Yet the proof is

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I found location of twin prime number. I will want need some help A belong to integers then, A is not equal to BC+B+C then, A is infinite Please say this statement is right/wrong. If statement is right please send it prove. If your proof is right then, I join your

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A quantum system has been found whose energy levels correspond to the zeros of the zeta function. This system was proposed on 30 of March 2017 in Physical Review Letters by Carl Bender of Washington University in St. Louis, Dorje Brody of Brunel University London and Markus Müller of the University

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I don't think they should be suppressed, and I think calling them "less good" is an oversimplification, but I agree with keeping them separate. They have a different character than the other references and are aimed at a different audience. Keeping them separate helps that audience to find material

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As with many other WP articles on physics and math, there is quite a high "baseline level" of knowledge required for the reader. This is counterproductive, as an encyclopedia is supposedly intended for people who do not already know everything about the subject (or else why would they look it up?).

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To save everyone from needing to wade through this: it seems that this is actually one of the better claimed proofs of RH. Although both sloppy in its notation and ultimately wrong—they're all wrong—when cleaned up, it does yield a valid heuristic that RH should be true -- a known heuristic, alas,

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i mean the riemann hypothesis as a concept is already pretty complex of a topic (no pun intended) so that level of knowledge of math as stated in the original post should be expected for the most part, and for those who dont know that stuff yet are wanting to learn the riemann hypothesis then they

768:

I completely agree with this separate subsection. Maybe some other works should be included in it also (I haven't gone through all references yet), but these four definitely are - euphemistically - "popular" expositions. And they are (not perhaps but certainly) "less good". In fact I wonder if we

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An “ambiguous” Riemann scenario would have to result in all of the corollaries being similarly ambiguous (for example, with something like Robin’s inequality, there would have to be instances where the inequality is possibly violated, but no algorithm can prove if it actually is, or if it merely

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In particular, two of the main functions of short descriptions are (1) to help disambiguate search results, on mobile, and (2) as part of annotated lists of links in see-also sections. In both cases (for instance, when searching for things named after Riemann or in mathematics articles where one

2196:

I'm sorry that you don't appreciate the importance (historically, and mathematically) of interesting systems such as Tag systems, and have channeled your disinterest into attacking the intention of my edits instead of reviewing the content I add. Sure, I happen to cite a lot of Wolfram material,

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Mathematics is a very incremental subject. Most advanced topics are difficult or impossible to understand without first understanding a pile of precursor topics which a typical person won't be familiar with. In the case of the Riemann hypothesis a reader who has no knowledge of complex analysis,

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o mathematician has publicly commented on his proposed proof. This has not been because of any lack of effort on KE’s part. Several eminent math journals have refused to accept his paper for review or, in at least one case, have replied with a dismissive single paragraph review that, strangely,

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The arXiv moderators classified this one as "General Mathematics (math.GM)". That generally means they thought it was junk. The long version history is also a bit of a red flag. I have no specific knowledge of what might be wrong with it, though. In any case we'd need secondary sources by other

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from 2017, yet another attempt? I'm sure it isn't a sound proof or I would have heard of it via other channels, but I was hoping to somewhere find an explanation of what's wrong with this one. Arxiv has some reputation, but I think the short answer would be to file it somewhere within the eight

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No. Until an article is peer-reviewed AND published by a reliable journal (in principle it should be reviewed by MathSciNet), it is not appropriate to mention it here. The fact is that version 10 of this preprint is now more than 2 years old and is not mentioned by MathSciNet: this is not very

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that they must be true. The actual construction of the Turing machines mentioned in the article are entirely within citations in the article. I similarly left a citation to an article which shows the actual construction of the tag system I was referencing. Could you please suggest ways I could

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What part of question did you not understand? It seems clear to me that the question revolved around the historical reasons for choosing s. While it goes without saying (which makes me wonder why you felt the need to point it out) that the choice of variable (not "letter") does not effect the

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Any chance you'd be willing to put up a PDF copy? The PNG method is quite inconvenient and slow. If you're not willing to make one generally available, you can email me a copy through Knowledge. I can't promise I will make any cogent comments, but parts of it do look rather interesting.

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immediately obvious to me where to fit it in. Now, the thing that made me bring this up is the treatment in the article of this result of Dudek. From what I can tell, this is a mild improvement of earlier work by Ramaré and Saouter (which itself builds on earlier work). It looks a bit

1222:. I hesitate to include the result in the Wiki article before it is peer reviewed, but it's worth to keep an eye on it. If their method turns out to be valid then there is further room for improvement: As they mention in footnote 2 on p.20, they were able to push the bound on the length 802:

I almost agree to conservation. Rather reluctantly concerning Derbyshire's book. But I don't agree at all concerning Sabbagh's books. I just moved in the new subsection his other book on the subject (also published in 2003…), which is not reviewed by MathSciNet and Zbl (and not even

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Sorry, my bad. Although I would have preferred to have the explanation even earlier than that in order not to lose faith, I guess I am oversensitized by all the other occurrences of unexplained or unlinked-to terminology that I have encountered elsewhere. Here, statement withdrawn.

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are an infinate number of primes.... so proving infinate fingers may be a step. I do apologize if I'm an idiot. I'm no maths whiz but for 20 years this problem has held me in it's grip. My only wish is for SOMEONE to prove, or disprove OR fall into Gödel's incompleteness theorems.

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Are you talking about result just above (11) in that paper? It allows o(x/log^4 x) exceptions, so the largest prime gaps could be larger. In fact even (11) itself can't show sqrt-sized gaps: set y = sqrt(x) and note that there could be on the order of log^2 x gaps of this size. -

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I'd never given this much thought until now, but it is clear that there is no generally accepted way of specifying the base of a logarithm, and that a certain amount of personal preference becomes involved. Pretty much all scientific calculators use the scheme in the Imgur

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here. Opeyemi Enoch's claimed 2015 proof fizzled out and hasn't been heard of for a long time. Kumar Eswaran has managed to pick up media coverage for his claimed proof, but this is not the same as convincing other mathematicians and winning the Clay Mathematics Institute

3225:, as part of a stronger but more specialized result. See Granville's "Harold Crámer and the distribution of prime numbers" for a discussion of the history. It seems strange to me that the article mentions the former but not the latter. Perhaps I am missing something? 3052:

might see this in a see-also section) the fact that this is mathematical is a given, and the fact that it's a conjecture is so vague as to be meaningless and unhelpful. Putting them both together adds pleonasm to the mix: conjectures are always mathematical. So

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very accessible — amazingly so. It uses no theorem or result that was discovered, say, after 1930. I, a professor of mechanical engineering, had no trouble following the details of the proof after revising my knowledge of undergraduate complex analysis...

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It may be the only argument but it's a strong argument. Log is much more standard in this area. "ln" is hard to distinguish from "1n" or "In", especially in text-based math formatting which we sometimes use. As for ISO, pfeh. Nobody follows ISO (see e.g.

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Good morning @David Eppstein, Sorry, yes you're right: the plot cuts off at 30. Can we provide a better plot? The current one seems misleading, showing zeros along the red line at 1, 2x near 14, 2x near 21, 2x near 25, and 1x just under 30. Thanks,

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The current shortdesc that you have reverted to violates point #1 because it attempts to be a definition. The fact that "mathematical conjecture" might be a suitable shortdesc for many articles does not make it unsuitable for this article. Best,

2794:. A proof of the Riemann hypothesis would be the greatest mathematical discovery in some time and because of that plenty of people have falsely claimed to have proved it. A real proof would generate far more coverage including from better sources. 2201:

a read, it might convince you of the importance of these less-appreciated systems. In the meantime, could another editor comment on the possible addition of a statement regarding Tag systems in this page, and whether Eppstein is editing from a

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Having watched the talk (and followup questions) live with several people mildly knowledge in the area, I do not strongly believe that Atiyah has successfully proved it, and agree with David Eppstein that we should wait for reliable sources.

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by MathSciNet!). Here is journalist, who is writing vulgarization on about everything you can think of, who is not a specialist of the subject, who is not even a mathematician, even in a very large acception of the term, and who publishes

3467:. (The part of our article that states "A related bound was given by Jeffrey Lagarias in 2002" is also of this form.) That means that if RH is false, it is provably false, but does not imply provability in the case that it is true. — 3545:

Instead of "The Riemann hypothesis is concerned with the locations of these nontrivial zeros, and states that..." I would write "The Riemann conjecture is concerned with the locations of these nontrivial zeros, and states that..."

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being a near miss, and 3., conversely, it is also possible to show that there is no way to prove that _all_ of the “candidate zeroes” are near misses). If 1., 2., and 3., are all true, this would make the RH permanently ambiguous.

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what is indeed clearly a conjecture concerning a subject that is indeed clearly mathematics. A better way to be useful would be to provide a concise and elegant formulation conveying the same information - no more, but no less. --

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to Wolfram to articles. And the fact that a computationally universal system can verify a counterexample to Riemann is not something that needs a tag system to construct. A tag system is merely an obfuscated way of doing it.

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looks like it has some interesting information to add to this article’s possible consequences section. However, it warns that it hasn’t been peer reviewed, so I don’t know if it’s appropriate to add information from it yet?

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You didn't see the sentence "The function Li occurring in the first term is..." ? It's a few lines down, but all of the lines between the formula and that sentence are also explanations of other parts of the same formula.

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Platt's work (2011 and later) should be added. Also, shouldn't we say something about the degree of rigour of some computations? I've heard that Gourdon-Demichel is a bit ropey on this point, due to non-rigorous sampling.

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brings up a 404 when I try to navigate to it. I did a quick look for it, but I wasn't 100% sure exactly which book it was supposed to be. Perhaps someone more knowledgeable than me can point the link towards a working

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past to publish rubbish in fairly good journals with peer-(not too careful)-reviewing. Anyway, after such insane claims in his preprints (clearly never to be printed…) I would be very careful before citing his paper.

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typeface, it might not be as easy to read. The word Ill can also suffer from this problem. The previous word is ill with a capital I, but it is very hard to distinguish from the Roman numeral III (3) when typed like

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Example from this article: in the section "History", the function "Li" is introduced without any explanation or even link to an explanation. The term "Li" is short enough to have two meanings in math listed in WP:

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I think its called the Riemann hypothesis because that's how it's used: as an extra hypothesis to prove results that would otherwise be unattainable. Regardless, it's the common name so we're not changing it. -

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This needs vastly better sourcing before it's included here. Both those articles claim that the solution to the Riemann hypothesis "could open the doors for the use of primes in cryptography" (as if that wasn't

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should not suppress these references from the article. None of the authors is a specialist of the subject. Sabbagh is not even a mathematician, and his book is his one and only work reviewed by MathSciNet (by

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infinite series or number theory isn't going to get very far, and that includes almost everybody who hasn't studied mathematics at university level. We could write an article along the lines of the ones in

2468:"scientific calculators", BTW, my calculator also has log for log_10 but it also has normal log_x^y that I always use. "log for log_e" No. This is not a scientifical article. For example, WHAT is this? 2158:

improve my edit, such as formatting the construction of the tag system in a Wiki-friendly manner, or perhaps this information belongs on a different page, instead of striking down valuable additions?

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which tries to explain the topic and underlying concepts to people who have no mathematical background, but it would have to be about as long as this article and it would need to be a separate page.

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page, there is a section on notable examples which states that a Turing Machine has been constructed which halts iff the RH is false. These statements are not vacuous even though it follow from the

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I have to agree with David Eppstein, the statement added is pretty trivial and if the best source available is a passing mention in a blog then it's not significant enough to include here anyway.

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We don't write articles based on viewership trends. There are an awful lot of attempted proofs of the Riemann Hypothesis which have not been accepted, so far this isn't distinguishable from them.

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Has this possibility been seriously considered (or, alternatively, ruled out?) The article should probably mention any “grey area” the Riemann hypothesis has, if in fact there actually is any.

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Your claim that it doesn't list the smaller zeros is factually incorrect. The three smallest are in the caption of the lead image of the article, and more are in the "Gram points" section. —

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Those are not zeros. They have imaginary part zero (the blue curve) but nonzero real part (the red curve), or vice versa. The zeros are where both colors cross the axis at the same point. —

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2A02:587:4114:9400:486E:F7D4:172C:1629 should speak more clearly. In the theory of analytic functions, all zeros are equally important. He has just volunteered for the task of connecting.

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people about it in order to add coverage of it here; there's a place in the world for cataloguing all the crank proofs of crank-magnet topics, but this Knowledge article isn't it. —

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gets it better in the first line: "Where are the zeros of zeta of s?" But maybe that's too informal. How about "Conjecture on zeros of the zeta function", exactly 40 characters? —

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Also lots of computer scientists use lg for log_2. In any case this is a mathematics article and mathematicians use log for log_e; that's the convention we should be following. —

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regarding his clearly strong bias against Wolfram material, which is hurting the neutrality of articles like this by keeping out interesting, factual, well-supported edits?

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This article seems to consider only two possibilities: either that the RH is true and we can easily prove it to be so, or that it is false and we can easily prove that.

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Did you just use imgur? Really? Anyway, log is implying that you should write the base, WHICH ONE cannot do on a calculator (still using it in 2021??). Full stop. See

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On 14 June 2017, N. Robles and K. Pratt have submitted a paper that claims to improve the lower bound for the proportion of zeros on the critical line to 41.49%. See

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for a more egregious example of ISO logarithm-notation that is best avoided). Consistency can be achieved by getting rid of stray instances of ln from the article. —

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I stand by the edit summary saying that "mathematical conjecture" is too vague. It needs a bit more detail and I will go along with what others think is suitable.--

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The only argument in favor of "log" seems to be that "log" is more accepted in the field of number theory. I think this argument weighs less than the previous two.

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promising. (The author is credited by MathSciNet with one single other published paper, which addresses a similar subject: Ramanujan J.59(2022), no.3, 745–755).--

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Oh yes I see: this guy claims a proof of the Riemann Hypothesis, and a "simple and correct" proof of Fermat's last theorem as well... This settles the matter! --

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other than 1" do you think fails to be a proper explanation? Or did you mean, why does our article use that particular letter for the argument, rather than

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The interest of other mathematicians in Atiyah's claimed proof seemed to fizzle out quickly. It is quite a long time ago now and the prize offered by the

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is yet another website that accepts pretty much anything, and people have to pay for the privilege of doing so ($ 400 to $ 850 according to the source).--

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who credits Turing 1939 for first studying it and Kreisel 1958 for proving that RH is equivalent to statement that some decidable property holds for all

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Thanks IanMacM; in my experience with mathematical English, "none are" is much more common than "none is" (in agreement with David Eppstein's revert). --

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On the third paragraph it would be better to use "conjecture" instead of "hypothesis". This is a conjecture and when proved it will become a theorem.

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commenting on the attempt of Louis de Branges to prove the Riemann Hypothesis. How can I bring it to the attention of those who would be interested?

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Anyone think a "In popular culture" section would be appropriate for this very serious article? Wolfram has three and I'm assuming there are more:

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Could you please briefly indicate in the caption where we can find the zeros in the plot, if it is not at crossings for zero values? Thank you,

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mathematics, it may not have been arbitrary. Do you know that it was arbitrary for sure? What is your source and why didn't you provide it?

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I just came here searching for this topic. Anyway, since ln is a bit confusing and there's not consensus on the meaning of log, shouldn't log

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Wow, I would never have thought that it would distinguish between adding a ping to an existing edit and making a new edit with a ping. OK. -

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It was based on the comments of the seven reviewers and responses of the author that the committee concluded Easwaran’s proof as correct...

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As far as I can tell, anyone who might have an informed opinion about this is saying "no comment" until details become available. I agree,

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showing how not to do it. When something like this is worth mentioning, it can usually be incorporated into the main body of the article.--

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Whatever gives you the idea that Knowledge must follow ISO? I don't know of any policy, guideline, or other precedent that would say so. —

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Probably not much, but it was given as an example. The key issue is whether to use ISO notation, which specifies ln for logs in base

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Thanks,of course that was silly of me. Perhaps we can indicate this explicitly, to help other mistaken fools like me.Thanks again,

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Looking at the relationship between RH and prime gaps: It is true that Crámer proved around 1920 that the size of a prime gap is

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on this subject that is readable by them, and helps mathematicians avoid material that is too popularized to be useful to them. —

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attempted proofs currently included in the article. (I wish I were sufficiently mathematical to be able to do so, but...)

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that such sections are a waste of time and tend to fill up with uninteresting, unsourced, and insignificant anecdotes. —

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or whatever? If so, you do realize that the choice of letter is arbitrary and does not affect the mathematics, right? —

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Someone added a bunch of junk to this page, which could be AI-generated but is obviously inappropriate regardless.

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For this purpose, there is absolutely no reason to depict the complex plane with anything but 1:1 aspect ratio.

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It's a number theory article, of course it should follow number theory conventions and use log rather than ln. -

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poorly explained, and it doesn't even have a list of some of the smaller zeroes of zeta(s) on the critical line.

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Why should this be relevant? How much use do you think research mathematicians make of scientific calculators? —

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Compliance with standards: ln is unambiguous contrary to log, probably more widely used, and recommended by ISO.

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Just in case anyone cares that readers understand what is written here, this article needs a great deal of work.

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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for natural- or integer-valued variables. I think this usage came from its use here with the zeta function. -

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should urge against this arbitrary judgement of some sources to be "popular" (and thus, less good perhaps?)

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Something carefully written should be added as the number of viewers jumped from a few thousands to 50K.

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https://www.cambridge.org/engage/coe/search-dashboard?authors=Frank%20Vega&sortBy=PUBLISHED_DATE_DESC

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A heuristic which is also very well known to the point where a variant of it is already in this article.

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Sorry for asking something that's not really related to Knowledge, but here goes. I recently put on line

3176:(assuming RH). But it is also true that he went on to show around 1930 that the size of a prime gap is 2723: 2587:

See arguments above about following standard notation rather than making up notation that nobody uses. —

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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Mainstream media outlets, even higher quality ones, aren't great sources for mathematical content, see

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I. Good and R. Churchhouse, The Riemann Hypothesis and Pseudorandom Features of the Möbius Sequence,

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https://en.wikipedia.org/search/?title=Riemann_zeta_function&diff=1034012285&oldid=1034010066

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indeed on ArXiv (labelled GM), but since partly under a pseudonym they were withdrawn by the admin:

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log_e", so what is correct? I think you need to add "USA" there too. Anyway, Knowledge is neither.

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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I agree that "Conjecture on zeros of the zeta function" is much better than my attempt. Thanks!

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This issue is surveyed by Matiyasevich "The Riemann hypothesis from a logician's point of view"

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before doing mass systematic removals. This message is updated dynamically through the template

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My suggestion is to explain or to reference what 's' stands for in the Riemann zeta function.

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I've updated it to a working link for the same book under a slightly different title and date,

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I am also (slightly) surprised by this blind hosting of Cambridge University Press. But well,

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The edit was not an improvement, for the reasons DE mentioned in his original edit summary. --

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could be reached. This in turn would further improve the lower bound on the number of zeros.

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I hope that this picture can be replaced by one with the appropriate aspect ratio oof 1:1.

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at the time. There are suggestions below for improving the article. If you can improve it,

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I’m surprised though, because I assumed Cambridge University Press was a reputable source.

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problems in mathematics; one of them, in fact, is the problem of deciding whether a given

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Note that it is often said that Levinson produced a proof for 33.33% and Conrey for 40%.

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For those following along at home, Floridada has now been blocked, as one member in a

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https://www.wired.com/2017/04/maths-1000000-question-isnt-just-mathematicians-anymore/

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If you found an error with any archives or the URLs themselves, you can fix them with

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sections aren't banned, but they can be enormous trivia magnets, and can end up like

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Mazur, Barry; Stein, William (2014), Primes. What is Riemann's hypothesis - the link

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The Science Publishing Group (which is the editor of this journal) is contained in

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However, as Kurt Gödel showed, sometimes things aren’t so cut-and-dried. There are

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and should not attempt to define the article's subject nor to summarise the lead.

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ln is log_e, lg is log_10 and log is log_2. That is common and how it should be.

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online facility where anything can be published with the appropriate payment.--

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http://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.17.pdf

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https://www.cambridge.org/engage/coe/article-details/62d118f6724581cd5d9721dc

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This article contains a great deal of advanced material, in almost all cases

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and there is a good deal of discussion about what it is. Since there is some

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and lasts 49 minutes. The audience and the press seemed less than impressed

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try to connect mathematically the trivial zeros to the non trivial ones

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if you haven't done so. Two key quotations (emphasis in the original):

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I think "ln" is a better notation than "log" for the following reasons:

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is a sort of standard choice for complex-valued variables, just like

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books on the Riemann hypothesis the same year. This is not serious.

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https://web.archive.org/web/20131005173705/http://www.zetagrid.net/

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because I find their content very interesting. I suggest you give

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The article includes a picture of zeta(1/2 + it) for -N ≤ t ≤ N.

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websites, and these are not accepted by the academic community.--

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Do you think the one paper that MathSciNet published is legit?

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to me to list the result with the current level of context.

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International Journal of Theoretical and Applied Mathematics

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When you have finished reviewing my changes, please set the

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Riemann's original article is linked as an illustration at

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Knowledge is not the place to do this, as it cannot accept

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All prior and subsequent edits to the article are noted in

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Consistency: At present this article uses both log and ln.

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for additional information. I made the following changes:

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and log for base 10, so I'm not sure if this is correct.

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I would not object to mentioning this in the article.

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of Western Ontario. See this general audience article:

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As pointed out previously, Knowledge cannot help with

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https://en.wikipedia.org/Logarithmic_integral_function

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This is an important illustration for this article.

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so there is no need to use an alternative wording.--

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Most scientific calculators use ln for logs in base

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On the Number of Primes Less Than a Given Magnitude

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http://mathworld.wolfram.com/RiemannHypothesis.html

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One of the references points at a non-existent page

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The conjecture that there are infinitely many 1220:http://www.math.uiuc.edu/~nirobles/research.html 33:for general discussion of the article's subject. 3797:Knowledge level-4 vital articles in Mathematics 2792:Exceptional claims require exceptional sources 889:This message was posted before February 2018. 2876: 2825: 2784:Knowledge:Reliable sources#News organizations 174: 8: 1774:name for solution for twin prime conjecture 1542:The video of Atiyah's lecture is on YouTube 2180:Knowledge is not an obfuscated code contest 1797:is also beyond the scope of this article.-- 1299:{\displaystyle \theta <{\tfrac {6}{11}}} 1826: 1581: 1386: 1357: 1334:{\displaystyle \theta <{\tfrac {4}{7}}} 1085: 1019: 996: 968: 839:I have just modified one external link on 272: 3447: 3442: 3436: 3416: 3206: 3193: 3181: 3157: 3145: 2070:Quality is more important than quantity. 1899: 1879: 1855: 1319: 1311: 1284: 1276: 1249: 1247: 1227: 3749:...Well, and in fact his complete works 2786:. This particular article seems to be a 2706:should work. It's listed as reliable at 1511:there is no need to rush to include this 1486:here, wait and see is the best policy.-- 1210:Proportion of zeros on the critical line 3822:Articles linked from high traffic sites 3817:Featured articles on Mathematics Portal 3787:Knowledge vital articles in Mathematics 3483:2600:1014:B07A:D001:F13B:C6F7:2888:1A08 3387:2600:1014:B07A:D001:F13B:C6F7:2888:1A08 3014:A short description is not a definition 2963: 2173:Floridada appears to exist only to add 274: 233: 2337:2A01:CB00:A34:1000:ED0E:D7C1:D5BD:64BC 2303:farm of Wolfram-promoting sock-puppets 1722:I solved them . I want to submit them 1003:2A02:587:4114:9400:486E:F7D4:172C:1629 698:http://modular.math.washington.edu/rh/ 571:https://en.wikipedia.org/Polylogarithm 505:January 2016: new year, same old story 3802:B-Class vital articles in Mathematics 878:to let others know (documentation at 7: 3538:Conjecture is better than hypothesis 2838:Dr. Easwaran's area of expertise is 1216:https://arxiv.org/pdf/1706.04593.pdf 1179:2001:44B8:266:D05:85D0:EEF3:C950:5AC 1041:https://arxiv.org/pdf/1602.03553.pdf 327:This article is within the scope of 1833:2A02:A455:91CE:1:6570:9FA9:6C2:B880 263:It is of interest to the following 23:for discussing improvements to the 3439: 3002:Each short description should: be 2996:short description instruction page 2466:https://en.wikipedia.org/Logarithm 14: 3812:Top-priority mathematics articles 3218:{\displaystyle o(\log ^{3}p_{n})} 2824:provides some necessary details, 1264:{\displaystyle {\tfrac {17}{33}}} 843:. Please take a moment to review 347:Knowledge:WikiProject Mathematics 3782:Knowledge level-4 vital articles 3374:number is actually zero or not. 3008:no more than about 40 characters 2871:His brother is quite miffed and 2828:the proof developed by Easwaran. 1743:predatory open-access publishing 1077:An "In Popular Culture" section? 1039:Is this a good place to mention 461: 414: 350:Template:WikiProject Mathematics 314: 304: 290: 276: 243: 234: 45:Click here to start a new topic. 2259:https://www.stephenwolfram.com/ 2133:Reverted edit about Tag systems 367:This article has been rated as 3792:B-Class level-4 vital articles 3745:21:29, 13 September 2024 (UTC) 3726:15:44, 13 September 2024 (UTC) 3709:10:10, 13 September 2024 (UTC) 3695:03:15, 13 September 2024 (UTC) 3674:18:36, 12 September 2024 (UTC) 3658:13:25, 12 September 2024 (UTC) 3630:made with a 1:1 aspect ratio. 3561:The Riemann hypothesis is the 3212: 3186: 3163: 3150: 2114:Category:Introductory articles 1718:Solution of Riemann hypothesis 1612:06:45, 25 September 2018 (UTC) 1596:06:19, 25 September 2018 (UTC) 1576:00:21, 25 September 2018 (UTC) 1567:17:18, 24 September 2018 (UTC) 1538:09:20, 24 September 2018 (UTC) 1523:03:41, 22 September 2018 (UTC) 1504:02:23, 22 September 2018 (UTC) 1: 2832:only seven responded on time. 2199:the article I initially cited 1996:21:00, 9 September 2022 (UTC) 1978:. It is evident that he used 1970:20:22, 9 September 2022 (UTC) 1939:16:59, 9 September 2022 (UTC) 1924:18:32, 13 November 2019 (UTC) 1841:11:36, 13 November 2019 (UTC) 1815:11:21, 16 February 2019 (UTC) 1784:08:13, 16 February 2019 (UTC) 1763:07:34, 20 December 2018 (UTC) 1732:07:28, 20 December 2018 (UTC) 1696:07:24, 10 February 2020 (UTC) 1670:02:17, 10 February 2020 (UTC) 1656:02:07, 10 February 2020 (UTC) 1641:01:37, 10 February 2020 (UTC) 1157:17:29, 25 February 2017 (UTC) 1124:17:02, 25 February 2017 (UTC) 1104:15:45, 25 February 2017 (UTC) 1011:21:11, 17 December 2016 (UTC) 730:19:51, 11 February 2016 (UTC) 711:19:09, 11 February 2016 (UTC) 341:and see a list of open tasks. 42:Put new text under old text. 3807:B-Class mathematics articles 3456:{\displaystyle \Pi _{1}^{0}} 2625:New claimed proof from India 661:09:10, 2 February 2016 (UTC) 618:08:57, 2 February 2016 (UTC) 603:08:04, 2 February 2016 (UTC) 587:07:31, 2 February 2016 (UTC) 555:22:43, 30 January 2016 (UTC) 535:09:29, 15 January 2016 (UTC) 515:Pioneer Scientific Publisher 494:Review: September 19, 2006. 3491:13:06, 15 August 2023 (UTC) 3477:06:40, 15 August 2023 (UTC) 3395:02:43, 15 August 2023 (UTC) 3353:06:48, 1 October 2022 (UTC) 3332:06:39, 1 October 2022 (UTC) 3318:06:35, 1 October 2022 (UTC) 3303:06:34, 1 October 2022 (UTC) 2945:12:48, 13 August 2021 (UTC) 2931:13:26, 13 August 2021 (UTC) 2597:12:13, 20 August 2023 (UTC) 2583:12:06, 20 August 2023 (UTC) 2573:be preferable for clarity? 1459:13:38, 13 August 2018 (UTC) 1437:12:36, 13 August 2018 (UTC) 1405:11:08, 13 August 2018 (UTC) 1242:of Feng's mollifier beyond 1034:13:14, 3 January 2017 (UTC) 686:13:41, 3 January 2017 (UTC) 436:, a high-traffic website. ( 50:New to Knowledge? Welcome! 3843: 3608:12:29, 26 April 2024 (UTC) 3583:18:00, 24 April 2024 (UTC) 3556:17:48, 24 April 2024 (UTC) 3522:has cleaned up the mess. — 3280:08:12, 14 April 2022 (UTC) 3257:05:20, 14 April 2022 (UTC) 3235:16:33, 13 April 2022 (UTC) 3124:06:55, 28 March 2022 (UTC) 3110:06:51, 28 March 2022 (UTC) 3096:06:48, 28 March 2022 (UTC) 3074:23:21, 27 March 2022 (UTC) 3047:21:37, 27 March 2022 (UTC) 3031:21:09, 27 March 2022 (UTC) 2972:Mathematics of Computation 2315:19:22, 12 March 2021 (UTC) 2296:19:13, 12 March 2021 (UTC) 2279:19:10, 12 March 2021 (UTC) 2245:19:26, 12 March 2021 (UTC) 2230:18:57, 12 March 2021 (UTC) 2216:18:07, 12 March 2021 (UTC) 2192:16:58, 12 March 2021 (UTC) 2168:16:10, 12 March 2021 (UTC) 2053:13:44, 15 April 2020 (UTC) 2038:06:17, 15 April 2020 (UTC) 1218:, and the authors page at 920:(last update: 5 June 2024) 836:Hello fellow Wikipedians, 822:22:39, 24 April 2016 (UTC) 798:18:04, 24 April 2016 (UTC) 783:17:12, 24 April 2016 (UTC) 763:15:18, 24 April 2016 (UTC) 633:17:32, 21 March 2022 (UTC) 3616:Picture could be improved 3532:23:59, 8 March 2024 (UTC) 3513:21:54, 8 March 2024 (UTC) 3409:10.1016/j.tcs.2019.07.028 2906:16:08, 29 June 2021 (UTC) 2852:15:52, 29 June 2021 (UTC) 2805:07:49, 29 June 2021 (UTC) 2766:06:54, 29 June 2021 (UTC) 2727:02:52, 29 June 2021 (UTC) 2683:18:02, 28 June 2021 (UTC) 2662:17:54, 28 June 2021 (UTC) 2565:08:00, 21 July 2021 (UTC) 2534:07:01, 21 July 2021 (UTC) 2520:06:57, 21 July 2021 (UTC) 2497:04:51, 21 July 2021 (UTC) 2483:03:17, 21 July 2021 (UTC) 2460:18:54, 20 July 2021 (UTC) 2446:18:32, 20 July 2021 (UTC) 2403:18:09, 20 July 2021 (UTC) 2389:15:38, 23 June 2021 (UTC) 2365:17:18, 13 June 2021 (UTC) 2353:Binary logarithm#Notation 2345:13:57, 13 June 2021 (UTC) 2127:18:59, 20 June 2020 (UTC) 2098:18:53, 20 June 2020 (UTC) 2083:17:03, 20 June 2020 (UTC) 1676:Millennium Prize Problems 1415:is another example of an 1372:07:21, 14 July 2017 (UTC) 1351:13:46, 16 June 2017 (UTC) 1069:21:14, 8 March 2022 (UTC) 1054:20:59, 8 March 2022 (UTC) 957:16:31, 21 July 2016 (UTC) 388: 366: 299: 271: 80:Be welcoming to newcomers 3169:{\displaystyle O(p_{n})} 2059:Pathetically bad article 1204:13:33, 30 May 2017 (UTC) 1187:13:25, 30 May 2017 (UTC) 861:http://www.zetagrid.net/ 373:project's priority scale 2008:None has, or none have? 1646:to be mentioned here. — 1235:{\displaystyle \theta } 832:External links modified 560:Please make it readable 330:WikiProject Mathematics 3827:Delisted good articles 3777:B-Class vital articles 3626:Unfortunately, it was 3465:arithmetical hierarchy 3457: 3425: 3359:Limits to provability? 3288:Plot of Re and Im part 3219: 3170: 2885: 2837: 1908: 1888: 1864: 1335: 1300: 1265: 1236: 643:Asking for suggestions 385: 75:avoid personal attacks 3458: 3426: 3220: 3171: 2642:Opeyemi Enoch in 2015 2633:: it is sourced here 2204:Neutral Point of View 1909: 1889: 1865: 1769:Twin prime conjecture 1336: 1301: 1266: 1237: 1110:I tend to agree with 718:http://wstein.org/rh/ 481:good article criteria 384: 250:level-4 vital article 100:Neutral point of view 3435: 3415: 3180: 3144: 2977:(1968), pp. 857–864. 2155:Church-Turing thesis 2149:. Similarly, on the 2147:has been constructed 1950:for real-valued and 1898: 1878: 1854: 1847:What part of "whose 1631:How about now? :) - 1479:has claimed a proof 1310: 1275: 1246: 1226: 1165:Quantum system found 901:regular verification 448:its revision history 353:mathematics articles 105:No original research 3640:Odd perfect numbers 3452: 2842:from these fields. 2143:User:David Eppstein 1776:Bipul Kumar Jaiswal 1724:Bipul Kumar Jaiswal 1417:online vanity press 1137:this cartoon parody 891:After February 2018 870:parameter below to 736:Popular expositions 3453: 3438: 3431:, the first level 3421: 3215: 3166: 2739:I'm worried about 2542:. When written in 1904: 1884: 1860: 1331: 1329: 1296: 1294: 1261: 1259: 1232: 945:InternetArchiveBot 896:InternetArchiveBot 841:Riemann hypothesis 741:sources. I think 469:Riemann hypothesis 425:Riemann hypothesis 422:On 20 March 2008, 395:Mathematics Portal 386: 322:Mathematics portal 259:content assessment 86:dispute resolution 47: 25:Riemann hypothesis 3606: 3424:{\displaystyle n} 3255: 2986:Short description 2929: 2868:is the 'roadmap'. 2864:is the proof and 2670:done in the 1970s 2387: 2110: 1968: 1907:{\displaystyle q} 1887:{\displaystyle x} 1863:{\displaystyle s} 1843: 1831:comment added by 1791:original research 1739:original research 1598: 1586:comment added by 1407: 1391:comment added by 1374: 1362:comment added by 1328: 1293: 1258: 1106: 1090:comment added by 1036: 1024:comment added by 1013: 1001:comment added by 986: 973:comment added by 921: 761: 499: 498: 495: 487:; it may then be 456: 455: 451: 409: 408: 405: 404: 401: 400: 228: 227: 66:Assume good faith 43: 3834: 3596: 3578: 3576: 3575: 3462: 3460: 3459: 3454: 3451: 3446: 3430: 3428: 3427: 3422: 3245: 3224: 3222: 3221: 3216: 3211: 3210: 3198: 3197: 3175: 3173: 3172: 3167: 3162: 3161: 3091: 3089: 3088: 2994:Please read the 2978: 2968: 2919: 2800: 2761: 2759: 2758: 2725: 2720: 2717: 2701: 2678: 2657: 2655: 2654: 2560: 2558: 2557: 2541: 2515: 2513: 2512: 2475:Valery Zapolodov 2441: 2439: 2438: 2424: 2395:Valery Zapolodov 2377: 2291: 2274: 2272: 2271: 2257:The sourcing at 2122: 2104: 2033: 2031: 2030: 1958: 1913: 1911: 1910: 1905: 1893: 1891: 1890: 1885: 1869: 1867: 1866: 1861: 1821:Explanation of s 1810: 1808: 1807: 1758: 1756: 1755: 1691: 1689: 1688: 1630: 1622: 1607: 1562: 1560: 1559: 1499: 1497: 1496: 1432: 1430: 1429: 1340: 1338: 1337: 1332: 1330: 1321: 1305: 1303: 1302: 1297: 1295: 1286: 1270: 1268: 1267: 1262: 1260: 1251: 1241: 1239: 1238: 1233: 1196: 1152: 1150: 1149: 955: 946: 919: 918: 897: 885: 771:D.R. Heath-Brown 760: 758: 746: 678: 672: 530: 528: 527: 493: 465: 464: 458: 445: 441: 418: 411: 391:selected article 355: 354: 351: 348: 345: 324: 319: 318: 308: 301: 300: 295: 294: 293: 288: 280: 273: 256: 247: 246: 239: 238: 230: 222: 179: 178: 164: 95:Article policies 16: 3842: 3841: 3837: 3836: 3835: 3833: 3832: 3831: 3767: 3766: 3642: 3618: 3573: 3571: 3569: 3540: 3501: 3433: 3432: 3413: 3412: 3372:computable real 3361: 3290: 3202: 3189: 3178: 3177: 3153: 3142: 3141: 3138: 3086: 3084: 3082: 2988: 2983: 2982: 2981: 2969: 2965: 2798: 2756: 2754: 2752: 2718: 2715: 2711: 2691: 2676: 2652: 2650: 2648: 2627: 2572: 2555: 2553: 2551: 2539: 2510: 2508: 2506: 2436: 2434: 2432: 2420: 2322: 2289: 2269: 2267: 2265: 2135: 2120: 2061: 2028: 2026: 2024: 2010: 1896: 1895: 1876: 1875: 1852: 1851: 1823: 1805: 1803: 1801: 1771: 1753: 1751: 1749: 1720: 1686: 1684: 1682: 1624: 1616: 1605: 1557: 1555: 1553: 1494: 1492: 1490: 1469: 1427: 1425: 1423: 1381: 1308: 1307: 1273: 1272: 1244: 1243: 1224: 1223: 1212: 1194: 1167: 1147: 1145: 1143: 1079: 1026:212.159.119.123 992: 990:Failed attempts 964: 949: 944: 912: 905:have permission 895: 879: 849:this simple FaQ 834: 756: 751: 747: 738: 694: 676: 666: 649:a paper I wrote 645: 562: 542: 525: 523: 521: 507: 462: 437: 352: 349: 346: 343: 342: 320: 313: 289: 286: 257:on Knowledge's 254: 244: 224: 223: 218: 121: 116: 115: 114: 91: 61: 12: 11: 5: 3840: 3838: 3830: 3829: 3824: 3819: 3814: 3809: 3804: 3799: 3794: 3789: 3784: 3779: 3769: 3768: 3765: 3764: 3763: 3762: 3761: 3760: 3759: 3758: 3757: 3756: 3747: 3718:203.220.166.72 3714: 3687:203.220.166.72 3679: 3650:203.220.166.72 3641: 3638: 3617: 3614: 3613: 3612: 3611: 3610: 3586: 3585: 3539: 3536: 3535: 3534: 3524:David Eppstein 3500: 3497: 3496: 3495: 3494: 3493: 3469:David Eppstein 3450: 3445: 3441: 3420: 3360: 3357: 3356: 3355: 3340: 3339: 3336: 3335: 3334: 3310:David Eppstein 3289: 3286: 3285: 3284: 3283: 3282: 3272:Russ Woodroofe 3260: 3259: 3227:Russ Woodroofe 3214: 3209: 3205: 3201: 3196: 3192: 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2001: 2000: 1999: 1998: 1988:David Eppstein 1916:David Eppstein 1903: 1883: 1872:complex number 1859: 1822: 1819: 1818: 1817: 1770: 1767: 1766: 1765: 1719: 1716: 1715: 1714: 1713: 1712: 1711: 1710: 1709: 1708: 1707: 1706: 1705: 1704: 1703: 1702: 1701: 1700: 1699: 1698: 1648:David Eppstein 1627:David Eppstein 1578: 1515:David Eppstein 1477:Michael Atiyah 1468: 1467:Michael Atiyah 1465: 1464: 1463: 1462: 1461: 1440: 1439: 1393:134.191.220.76 1380: 1377: 1376: 1375: 1327: 1324: 1318: 1315: 1292: 1289: 1283: 1280: 1257: 1254: 1231: 1211: 1208: 1207: 1206: 1195:Sławomir Biały 1166: 1163: 1162: 1161: 1160: 1159: 1127: 1126: 1116:David Eppstein 1078: 1075: 1074: 1073: 1072: 1071: 1061:David Eppstein 1037: 1015: 1014: 991: 988: 975:213.106.56.145 963: 960: 939: 938: 931: 864: 863: 855:Added archive 833: 830: 829: 828: 827: 826: 825: 824: 790:David Eppstein 754: 749: 737: 734: 733: 732: 722:David Eppstein 693: 690: 689: 688: 677:Sławomir Biały 644: 641: 640: 639: 638: 637: 636: 635: 595:David 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