List questions from zeta-functions

Published on 29 Oct 2019 - 11:09

224

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How to prove this series identity $\sum_{n=1}^{\infty}\left(\frac{1}{n}\sum_{k=n+1}^{\infty}\frac{1}{k^3}\right)=\frac{\pi^{4}}{360}$?

Published on 09 Nov 2019 - 1:14

120

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Is there any generic way to obtain $\sum_{n=0}^\infty \frac{1}{(kn+q)^s}$ from Riemann zeta function?

Published on 11 Nov 2019 - 2:46

237

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Does $\sum_{n=1}^\infty \frac{1}{\phi(n)^s}$ have a euler product?

Published on 25 Mar 2026 - 14:37

70

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Prove that, $\zeta(3)=\sum^{\infty}_{n=1}\frac{(-1)^{n+1}H_n^{\phi(2)}(2n+1)}{n(n+1)}$.

Published on 17 Nov 2019 - 13:58

88

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a contour integral involving Sign function related to Lerch Zeta function

Published on 17 Nov 2019 - 22:02

29

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show an oscillatory integral sequence is decreasing

Published on 20 Nov 2019 - 14:15

78

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Integral Test on An Open Ball

Published on 27 Nov 2019 - 7:00

101

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Understanding $\zeta(s)$ is Holomorphic

Published on 27 Nov 2019 - 8:02

96

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Implication of $\zeta(s)\ne 0$

Published on 01 Dec 2019 - 16:22

102

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Holomorphicity of the ratio of zeta functions

Published on 22 Mar 2026 - 20:10

103

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Closed forms of $f(s;q)=\sum_{k\ge1}\frac{(-1)^k}{k^s+q^s}$

Published on 02 Jan 2020 - 7:56

277

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Stronger asymptotics of the partial sums of the prime zeta function

Published on 04 Jan 2020 - 11:06

935

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What is the value of ζ(1)?

Published on 25 Jan 2020 - 1:39

78

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How to analytically continue the ‘two-dimension’ zeta function?

Published on 25 Mar 2026 - 14:21

List Question

Conjectural closed-form of $\int_0^1 \frac{\log^n (1-x) \log^{n-1} (1+x)}{1+x} dx$

How to prove this series identity $\sum_{n=1}^{\infty}\left(\frac{1}{n}\sum_{k=n+1}^{\infty}\frac{1}{k^3}\right)=\frac{\pi^{4}}{360}$?

Is there any generic way to obtain $\sum_{n=0}^\infty \frac{1}{(kn+q)^s}$ from Riemann zeta function?

Does $\sum_{n=1}^\infty \frac{1}{\phi(n)^s}$ have a euler product?

Prove that, $\zeta(3)=\sum^{\infty}_{n=1}\frac{(-1)^{n+1}H_n^{\phi(2)}(2n+1)}{n(n+1)}$.

a contour integral involving Sign function related to Lerch Zeta function

show an oscillatory integral sequence is decreasing

Integral Test on An Open Ball

Understanding $\zeta(s)$ is Holomorphic

Implication of $\zeta(s)\ne 0$

Holomorphicity of the ratio of zeta functions

Closed forms of $f(s;q)=\sum_{k\ge1}\frac{(-1)^k}{k^s+q^s}$

Stronger asymptotics of the partial sums of the prime zeta function

What is the value of ζ(1)?

How to analytically continue the ‘two-dimension’ zeta function?

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