# Top zeta and L-functions (Trending topics)

The following are the current most viewed articles on Wikipedia within Wikipedia's Zeta and L-functions category. Think of it as a What's Hot list for Zeta and L-functions. More info »

This is a beta release and so the figures may be a day or two out of date. We'd love to get your thoughts.

Rank Topic Wikipedia views
1 Riemann hypothesis 2,515
2 Riemann zeta function 1,347
3 Birch and Swinnerton-Dyer conjecture 382
4 Basel problem 281
5 Langlands program 223
6 Polylogarithm 166
7 L-function 110
8 Apéry's constant 107
9 Dirichlet series 93
10 Weil conjectures 89
11 Zeta function 88
12 Dirichlet's theorem on arithmetic progressions 88
13 Generalized Riemann hypothesis 86
14 Dirichlet character 82
15 Proof of the Euler product formula for the Riemann zeta function 77
16 Explicit formula 76
17 Dirichlet L-function 70
18 Dirichlet eta function 66
19 Euler product 58
21 Dirichlet beta function 50
22 Hurwitz zeta function 49
23 Zeta function regularization 48
24 Hasse–Weil zeta function 43
25 Multiplication theorem 37
26 Riemann–Siegel formula 36
27 Siegel zero 35
28 Zeta constant 34
29 Odlyzko–Schönhage algorithm 32
30 Local zeta-function 31
31 Hilbert–Pólya conjecture 30
32 Zeta function universality 27
33 Selberg zeta function 26
34 Hecke character 25
35 Lerch zeta function 24
36 Eichler–Shimura congruence relation 24
37 Artin L-function 23
38 Special values of L-functions 23
39 Equivariant L-function 22
40 Functional equation (L-function) 21
41 Riemann–Siegel theta function 20
42 Dedekind zeta function 18
43 Shimura variety 18
44 Prime zeta function 17
45 Lindelöf hypothesis 16
46 Apéry's theorem 15
47 Subgroup growth 14
48 Ihara zeta function 13
49 Li's criterion 13
50 Riemann Xi function 12
51 Brumer–Stark conjecture 12
52 Riesz mean 11
53 Clausen function 10
54 Zeta function (operator) 10
55 Stieltjes constants 9
56 Multiple zeta function 9
57 Shintani zeta function 9
58 Rankin–Selberg method 9
59 Riesz function 8
61 Rational zeta series 7
62 ZetaGrid 7
63 Montgomery's pair correlation conjecture 7
64 Selberg class 6
65 Goss zeta function 6
66 Grand Riemann hypothesis less than 5 views
67 Artin–Mazur zeta function less than 5 views
68 Minakshisundaram-Pleijel zeta function less than 5 views
69 Airy zeta function less than 5 views
70 Chowla–Mordell theorem less than 5 views
71 Lefschetz zeta function less than 5 views
72 Fekete polynomial less than 5 views
73 Stark conjectures less than 5 views
74 Weil's criterion less than 5 views
75 Hadjicostas's formula less than 5 views
76 Barnes zeta function less than 5 views
77 Witten zeta function less than 5 views
78 Matsumoto zeta function less than 5 views

# Encyclopedia

Zeta-functions and L-functions express important relations between the geometry of Riemann surfaces, number theory and dynamical systems. Zeta-functions, and their generalizations such as the Selberg class S, are conjectured to have various important properties, including generalizations of the Riemann hypothesis and various relationships with automorphic forms as well as to the representations of groups. The pursuit of the relationships comprises the Langlands program.

This category corresponds roughly to MSC 11M Zeta and L-functions: analytic theory in the American Mathematical Society's Mathematics Subject Classification.

## Pages in category "Zeta and L-functions"

The following 72 pages are in this category, out of 72 total. This list may not reflect recent changes (learn more).