192:
corresponding articles so that even the layperson is able to have an idea of how they are related. And this is of paramount importance, for there are analogous statements of the
Riemann Hypothesis for several of those classes, and this has implications on other conjectures. For example: Goldbach's weak conjecture can be derived from the Generalized Riemann Hypothesis, but the latter needs the Riemann Hypothesis to be proved for Dirichlet L-functions (or so I seem to have understood from the corresponding articles). However, Hecke L-functions were constructed to encompass Dirichlet L-functions. Does this mean that proving RH for Hecke L-functions proves Goldbach's weak conjecture as well? From what I could see in Knowledge, it seems that the answer is yes, but the leaps made from the word L-function to the word character to the word L-series create some confusion to laypeople like myself. Is it possible to say something of the kind: all Dirichlet L-functions are Hecke L-functions? I believe the general article on L-functions should be made into a departure point for all people who would like to know, even without understanding the mathematics, how concepts are inter-related. A good start would be to name all important classes of L-functions here.
84:
74:
53:
22:
214:
of what all these different L-function are! Generally speaking, only GRH is interesting for applications to traditional analytic number theory. We know very little about analytical properties of very general L-functions (even the location of the poles is difficult to pin down), and their theory for
191:
I am not a mathematician myself, and have no idea of what L-functions are. However, from browsing the
Knowledge I managed to understand that there are several classes of such functions: Hecke L-functions, Dirichlet L-functions, Dedekind set functions, etc.. I think much work is needed in all the
224:
Some indication that the domain is not always the complex plane, but can be much more general, would be nice (or have I missed it?). This should, of course, be late in the article, but should indicate how the situation changes in other fields.
215:
the most part has quite different flavor. Having said that, let me answer your specific question: yes, a notion of Hecke L-function is a (vast) generalization of the
Dirichlet L-function, but not as general as Artin or Langlands L-function.
140:
292:
130:
106:
287:
97:
58:
257:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
196:
Your request is very meaningful. Unfortunately, however, there are genuine mathematical difficulties involved. Forget about
33:
39:
83:
264:
230:
21:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
73:
52:
174:
The L-function should be defined (either technically or intuitively) and bolded at the start.
178:
226:
281:
275:
Last edited at 14:13, 2 September 2007 (UTC). Substituted at 02:16, 5 May 2016 (UTC)
254:
216:
175:
102:
166:
79:
165:
Historically, what does the L in L-function or L-series stand for? Lagrange?
267:
234:
219:
200:
even the layperson is able to have an idea of how they are related
181:
169:
15:
210:, certainly a very large number outside of number theory,
249:
101:, a collaborative effort to improve the coverage of
253:, and are posted here for posterity. Following
247:The comment(s) below were originally left at
8:
47:
49:
19:
263:needs a definition of some L-function
7:
95:This article is within the scope of
38:It is of interest to the following
293:High-priority mathematics articles
14:
255:several discussions in past years
115:Knowledge:WikiProject Mathematics
118:Template:WikiProject Mathematics
82:
72:
51:
20:
135:This article has been rated as
235:22:21, 16 September 2008 (UTC)
1:
268:14:13, 2 September 2007 (UTC)
109:and see a list of open tasks.
288:C-Class mathematics articles
187:A request for clarification
309:
220:06:35, 10 March 2007 (UTC)
262:
170:11:41, 13 July 2006 (UTC)
134:
67:
46:
250:Talk:L-function/Comments
208:even most mathematicians
141:project's priority scale
182:19:22, 8 May 2006 (UTC)
98:WikiProject Mathematics
28:This article is rated
121:mathematics articles
243:Assessment comment
90:Mathematics portal
34:content assessment
273:
272:
233:
155:
154:
151:
150:
147:
146:
300:
260:
259:
252:
229:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
308:
307:
303:
302:
301:
299:
298:
297:
278:
277:
265:Jakob.scholbach
248:
245:
227:Septentrionalis
189:
163:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
306:
304:
296:
295:
290:
280:
279:
271:
270:
244:
241:
240:
239:
238:
237:
205:
204:
203:
188:
185:
162:
159:
157:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
305:
294:
291:
289:
286:
285:
283:
276:
269:
266:
261:
258:
256:
251:
242:
236:
232:
228:
223:
222:
221:
218:
213:
209:
206:
201:
198:
197:
195:
194:
193:
186:
184:
183:
180:
177:
172:
171:
168:
160:
158:
142:
138:
137:High-priority
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
62:High‑priority
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
274:
246:
212:have no idea
211:
207:
199:
190:
173:
164:
156:
136:
96:
40:WikiProjects
112:Mathematics
103:mathematics
59:Mathematics
282:Categories
231:PMAnderson
161:Untitled
139:on the
30:C-class
217:Arcfrk
179:(talk)
36:scale.
167:Ninte
131:High
284::
176:MP
202:—
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.