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is quite tight, and there are many points that actually lie outside this image. However, the image does indicate their relative rarity. In short, this image indicates that although the divisor summatory function is quite random, it does seem to have rather well-behaved statistical properties, and
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runs horizontally down the center of the image. The histogramming is such that the areas which have a high density of points are colored red, progressively fading out to yellow, green, blue and finally black. Note that the bound
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with the leading asymptotic terms subtracted. That is, it is a graph of :<math>D(x)-x\log x - x(2\gamma-1)</math> where <math>D(x)</math> is the divisor summatory
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Properly speaking, the image is of the distribution of the values of the divisor summatory function, with each vertical slice being a
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This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
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If the file has been modified from its original state, some details may not fully reflect the modified file.
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If you think that a local copy of this file should be retained, then replace this
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Permission is granted to copy, distribute and/or modify this document under the terms of the
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If this file is freely licensed, but otherwise unsuitable for
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Please ensure that the file has a properly descriptive and unambiguous name
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455:-axis is scaled, so that, from bottom to top, the height of the image is
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with the leading asymptotic terms subtracted. That is, it is a graph of
659://en.wikipedia.org/Wikipedia:Text_of_the_GNU_Free_Documentation_License
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Click on a date/time to view the file as it appeared at that time.
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This licensing tag was added to this file as part of the GFDL
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seems to have a narrowing standard deviation as moving from
934:== Divisor summatory function== This graph illustrates the
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150:{\displaystyle \Delta (x)=D(x)-x\log x-x(2\gamma -1)}
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245:{\displaystyle D(x)=\sum _{n\leq x}d(n)}
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310:{\displaystyle \gamma =0.577\ldots }
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444:{\displaystyle \Delta (x)}
69:divisor summatory function
63:Divisor summatory function
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486:{\displaystyle 2x^{7/22}}
319:Euler-Mascheroni constant
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611:{\displaystyle x=10^{7}}
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578:{\displaystyle x=0}
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1001:GFDL files
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982:_error
949:File usage
908:500 × 500
884:Dimensions
808:Keep local
760:ineligible
628:User:Linas
422:values of
336:runs from
53:image/jpeg
27:File usage
881:Thumbnail
878:Date/Time
846:User:Fbot
756:copyright
697:License.
622:Licensing
528:±
430:Δ
326:histogram
305:…
296:γ
223:≤
216:∑
139:−
136:γ
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82:Δ
969:Metadata
927:contribs
32:Metadata
910:(58 KB)
895:current
890:Comment
772:blocked
332:-axis,
317:is the
284:is the
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302:0.577
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
