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Question on Difference Root representations of $\eta(2 n+1)$ and $\beta(2n)$ where $n\in\mathbb{N}$

score 89 · Answer 1 · 2026-03-25 07:15:34

89

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Question on Difference Root representations of $\eta(2 n+1)$ and $\beta(2n)$ where $n\in\mathbb{N}$

Published on 25 Mar 2026 - 7:15

score 250 · Answer 2 · 2021-08-09 15:45:00

250

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Prove that the infinite $\sum_{\text{ p prime}}\frac{1}{2^p}$ is an irrational number.

Published on 09 Aug 2021 - 15:45

score 121 · Answer 3 · 2026-03-25 07:15:32

121

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Question related to potential closed-form representation of Catalan's constant

Published on 25 Mar 2026 - 7:15

score 59 · Answer 4 · 2021-08-17 00:36:55

59

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Step in Apostol's IANT on Dirichlet Series

Published on 17 Aug 2021 - 0:36

score 53 · Answer 5 · 2021-08-18 13:37:01

53

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Summary of Dirichlet Series Convergence from Apostol's IANT

Published on 18 Aug 2021 - 13:37

score 190 · Answer 6 · 2021-08-18 14:52:40

190

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What do we know about the analytic continuations of Dirichlet series?

Published on 18 Aug 2021 - 14:52

score 52 · Answer 7 · 2026-03-26 01:34:59

52

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Variant of Möbius inversion: $b(n) = \sum_{d^2 \mid n} a(n/d^2) d^\alpha$

Published on 26 Mar 2026 - 1:34

score 137 · Answer 8 · 2021-08-21 20:43:06

137

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What is the abscissa of convergence of the series $\sum\limits_{n=1}^{\infty} (-1)^n \frac {1} {n^s}\ $?

Published on 21 Aug 2021 - 20:43

score 242 · Answer 9 · 2021-08-31 19:18:26

242

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Proof Riemann Zeta Series based on $\eta(s)$ has only one pole.

Published on 31 Aug 2021 - 19:18

score 275 · Answer 10 · 2021-09-03 04:10:28

275

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If the Dirichlet's eta function is conditionally convergent in the critical strip how can we ever compute its values there?

Published on 03 Sep 2021 - 4:10

score 115 · Answer 11 · 2021-09-03 21:40:16

Are there are other known functions that give the same set of zeros as the Riemann zeta function inside the critical strip besides $\eta(s)$?

score 223 · Answer 12 · 2021-10-20 02:08:39

223

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Prove $\sum_{d | n} \mu(d) (\log(d))^2=0$

Published on 20 Oct 2021 - 2:08

score 215 · Answer 13 · 2021-11-28 19:15:12

215

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Proof that Dirichlet series $\sum_{n=1}^{\infty}\frac{2^{\omega(n)}}{n^2}=\frac{5}{2}$

Published on 28 Nov 2021 - 19:15

score 151 · Answer 14 · 2021-12-21 23:11:30

151

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Proving $\prod_{n=0}^{\infty}\left(1+\frac{x}{a^n}\right)=\sum_{n=0}^{\infty}\frac{(ax)^n}{\prod_{k=1}^{n}(a^k-1)}$

Published on 21 Dec 2021 - 23:11

score 107 · Answer 15 · 2026-02-23 09:08:57

107

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Looking for table of special values of the Dirichlet $L$-function

Published on 23 Feb 2026 - 9:08

List Question

Question on Difference Root representations of $\eta(2 n+1)$ and $\beta(2n)$ where $n\in\mathbb{N}$

Prove that the infinite $\sum_{\text{ p prime}}\frac{1}{2^p}$ is an irrational number.

Question related to potential closed-form representation of Catalan's constant

Step in Apostol's IANT on Dirichlet Series

Summary of Dirichlet Series Convergence from Apostol's IANT

What do we know about the analytic continuations of Dirichlet series?

Variant of Möbius inversion: $b(n) = \sum_{d^2 \mid n} a(n/d^2) d^\alpha$

What is the abscissa of convergence of the series $\sum\limits_{n=1}^{\infty} (-1)^n \frac {1} {n^s}\ $?

Proof Riemann Zeta Series based on $\eta(s)$ has only one pole.

If the Dirichlet's eta function is conditionally convergent in the critical strip how can we ever compute its values there?

Are there are other known functions that give the same set of zeros as the Riemann zeta function inside the critical strip besides $\eta(s)$?

Prove $\sum_{d | n} \mu(d) (\log(d))^2=0$

Proof that Dirichlet series $\sum_{n=1}^{\infty}\frac{2^{\omega(n)}}{n^2}=\frac{5}{2}$

Proving $\prod_{n=0}^{\infty}\left(1+\frac{x}{a^n}\right)=\sum_{n=0}^{\infty}\frac{(ax)^n}{\prod_{k=1}^{n}(a^k-1)}$

Looking for table of special values of the Dirichlet $L$-function

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