Question

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

score 112 · Answer 1 · 2026-02-23 07:20:46

112

Views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

Published on 23 Feb 2026 - 7:20

score 60 · Answer 2 · 2026-02-23 07:21:33

60

Views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

Published on 23 Feb 2026 - 7:21

score 276 · Answer 3 · 2023-11-03 14:51:52

276

Views

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Published on 03 Nov 2023 - 14:51

score 63 · Answer 4 · 2023-11-15 00:52:09

63

Views

Asymptotics for the number of $n\le x$ which can be written as the sum of two squares. Is Perron's formula applicable?

Published on 15 Nov 2023 - 0:52

score 36 · Answer 5 · 2026-03-25 21:22:52

36

Views

$ 0 = 1 + \sum_{n=2}^{\infty} \frac{n^{-s}}{\ln(n)} \implies Re(s) \leq \frac{1}{2}$?

Published on 25 Mar 2026 - 21:22

score 18 · Answer 6 · 2026-03-19 23:08:46

18

Views

$ f(s) = 1 + \sum_{n=2}^{\infty} \frac{n^{-s}}{p_n}= 0$?

Published on 19 Mar 2026 - 23:08

score 55 · Answer 7 · 2026-02-23 07:19:22

55

Views

"Mollifier" of the Dirichlet L-function

Published on 23 Feb 2026 - 7:19

score 88 · Answer 8 · 2023-12-15 10:02:18

88

Views

Dirichlet series of an elementary function

Published on 15 Dec 2023 - 10:02

score 73 · Answer 9 · 2024-01-06 22:49:08

73

Views

A question about Landau’s theorem for Dirichlet series and integrals

Published on 06 Jan 2024 - 22:49

score 47 · Answer 10 · 2024-01-08 20:59:27

47

Views

Gamma integral in Dirichlet L-series

Published on 08 Jan 2024 - 20:59

score 99 · Answer 11 · 2024-01-19 23:38:47

99

Views

Proof of $\sum_{n=1}^\infty a_n n^{-s} = s\int_1^\infty A(x) x^{-s-1}\, dx$ and $\limsup_{x\to\infty} \frac{\log|A(x)|}{\log x} = \sigma_c$

Published on 19 Jan 2024 - 23:38

score 171 · Answer 12 · 2026-03-25 22:05:41

171

Views

Proof of Theorem 1.1 of Analytic Number Theory by Iwaniec & Kowalski

Published on 25 Mar 2026 - 22:05

score 66 · Answer 13 · 2024-01-25 11:04:17

66

Views

A question about Lemma 15.1 (Landau’s theorem for integrals) in Montgomery-Vaughan’s book

Published on 25 Jan 2024 - 11:04

score 358 · Answer 14 · 2015-01-14 18:51:43

How to prove $(\frac{1}{5^3}-\frac{1}{7^3})+(\frac{1}{11^3}-\frac{1}{13^3})+(\frac{1}{17^3}-\frac{1}{19^3})+...=(1-\frac{\pi ^3}{18\sqrt{3}})$

score 184 · Answer 15 · 2015-01-23 13:27:14

184

Views

Prove that this sequence of integers is on average equal to zero.

Published on 23 Jan 2015 - 13:27

List Question

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

Explore the relationship between $\sum\limits_{n = 1}^{2x} \frac{1}{{n^s}^x}$ and $\sum\limits_{n = 1}^{2x-1} \frac{(-1)^{n-1}}{{n^s}^x}$

Asymptotics for the number of $n\le x$ which can be written as the sum of two squares. Is Perron's formula applicable?

$ 0 = 1 + \sum_{n=2}^{\infty} \frac{n^{-s}}{\ln(n)} \implies Re(s) \leq \frac{1}{2}$?

$ f(s) = 1 + \sum_{n=2}^{\infty} \frac{n^{-s}}{p_n}= 0$?

"Mollifier" of the Dirichlet L-function

Dirichlet series of an elementary function

A question about Landau’s theorem for Dirichlet series and integrals

Gamma integral in Dirichlet L-series

Proof of $\sum_{n=1}^\infty a_n n^{-s} = s\int_1^\infty A(x) x^{-s-1}\, dx$ and $\limsup_{x\to\infty} \frac{\log|A(x)|}{\log x} = \sigma_c$

Proof of Theorem 1.1 of Analytic Number Theory by Iwaniec & Kowalski

A question about Lemma 15.1 (Landau’s theorem for integrals) in Montgomery-Vaughan’s book

How to prove $(\frac{1}{5^3}-\frac{1}{7^3})+(\frac{1}{11^3}-\frac{1}{13^3})+(\frac{1}{17^3}-\frac{1}{19^3})+...=(1-\frac{\pi ^3}{18\sqrt{3}})$

Prove that this sequence of integers is on average equal to zero.

Trending Questions

Popular # Hahtags

Popular Questions