Question

How do I find the residues of log(zeta(s))/s?

score 71 · Answer 1 · 2023-07-29 16:51:47

71

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How do I find the residues of log(zeta(s))/s?

Published on 29 Jul 2023 - 16:51

score 96 · Answer 2 · 2023-07-30 13:01:25

How to show that $\sum_{k=1}^{\infty}\frac1{k^s} = \frac{1}{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$

score 93 · Answer 3 · 2026-03-26 04:36:23

93

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Are the imaginary parts of these Riemann zeta related numbers equal?

Published on 26 Mar 2026 - 4:36

score 131 · Answer 4 · 2026-03-26 12:36:36

131

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Analytic continuation for $\zeta(-x)$ vs $\frac{1}{(1-x)^2}$ at $x=1$

Published on 26 Mar 2026 - 12:36

score 89 · Answer 5 · 2023-08-01 21:58:54

89

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Is there a general term for $\zeta((1+2n)/2)/\zeta((1-2n)/2)$

Published on 01 Aug 2023 - 21:58

score 147 · Answer 6 · 2023-08-05 06:01:37

147

Views

Find the value of the infinite series: $(1/3^2)+(1/3^3)+(1/3^4)+...+(1/5^2)+(1/5^3)+...+(1/7^2)+(1/7^3)+...+...$

Published on 05 Aug 2023 - 6:01

score 54 · Answer 7 · 2026-03-27 04:23:30

54

Views

Visual representation of Zeta Series in Real numbers

Published on 27 Mar 2026 - 4:23

score 81 · Answer 8 · 2026-03-26 08:03:21

81

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Does $\sum_\rho R(x^\rho) \sim \sqrt{x}/\log(x)$ assume the Riemann hypothesis?

Published on 26 Mar 2026 - 8:03

score 278 · Answer 9 · 2026-03-26 04:33:15

278

Views

Landau-Siegel zeros: Why can't they be found?

Published on 26 Mar 2026 - 4:33

score 495 · Answer 10 · 2023-08-14 19:24:30

495

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Extension of PDE's to critical strip

Published on 14 Aug 2023 - 19:24

score 109 · Answer 11 · 2026-03-25 18:50:38

109

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Questions on $f(x)=\sum\limits_{n=1}^{\infty} \frac{(-1)^n\, (2 n+1)}{2 n!}\, \pi^n\, \frac{\zeta''(-2 n)}{\zeta'(-2 n)}\, x^{-2 n}$

Published on 25 Mar 2026 - 18:50

score 435 · Answer 12 · 2023-08-16 13:32:11

435

Views

Integral: $\displaystyle\int_0^1\!\frac{x}{\operatorname{artanh} x} \, {\rm d}x\overset{?}{=}\frac{7\zeta(3)}{\pi^2}$

Published on 16 Aug 2023 - 13:32

score 84 · Answer 13 · 2026-03-25 18:50:38

84

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Questions on $g(x)=\sum\limits_{n=1}^\infty \frac{(-1)^{n+1}\, (2 n+1)}{n!}\, \pi^n\, \frac{\zeta'(2 n+1)}{\zeta(2 n+1)} x^{-2 n}$

Published on 25 Mar 2026 - 18:50

score 46 · Answer 14 · 2023-08-18 08:37:45

46

Views

Is there any closed form expression for this series involving $\coth$ function?

Published on 18 Aug 2023 - 8:37

score 45 · Answer 15 · 2023-08-19 16:30:28

45

Views

Reference request on formulas for the second-order derivative of the Riemann zeta function at integer values

Published on 19 Aug 2023 - 16:30

List Question

How do I find the residues of log(zeta(s))/s?

How to show that $\sum_{k=1}^{\infty}\frac1{k^s} = \frac{1}{\Gamma(s)}\int_{0}^\infty \frac{x^{s-1}}{e^x-1}dx$

Are the imaginary parts of these Riemann zeta related numbers equal?

Analytic continuation for $\zeta(-x)$ vs $\frac{1}{(1-x)^2}$ at $x=1$

Is there a general term for $\zeta((1+2n)/2)/\zeta((1-2n)/2)$

Find the value of the infinite series: $(1/3^2)+(1/3^3)+(1/3^4)+...+(1/5^2)+(1/5^3)+...+(1/7^2)+(1/7^3)+...+...$

Visual representation of Zeta Series in Real numbers

Does $\sum_\rho R(x^\rho) \sim \sqrt{x}/\log(x)$ assume the Riemann hypothesis?

Landau-Siegel zeros: Why can't they be found?

Extension of PDE's to critical strip

Questions on $f(x)=\sum\limits_{n=1}^{\infty} \frac{(-1)^n\, (2 n+1)}{2 n!}\, \pi^n\, \frac{\zeta''(-2 n)}{\zeta'(-2 n)}\, x^{-2 n}$

Integral: $\displaystyle\int_0^1\!\frac{x}{\operatorname{artanh} x} \, {\rm d}x\overset{?}{=}\frac{7\zeta(3)}{\pi^2}$

Questions on $g(x)=\sum\limits_{n=1}^\infty \frac{(-1)^{n+1}\, (2 n+1)}{n!}\, \pi^n\, \frac{\zeta'(2 n+1)}{\zeta(2 n+1)} x^{-2 n}$

Is there any closed form expression for this series involving $\coth$ function?

Reference request on formulas for the second-order derivative of the Riemann zeta function at integer values

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