Question

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

score 85 · Answer 1 · 2026-03-26 07:59:04

85

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Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Published on 26 Mar 2026 - 7:59

score 173 · Answer 2 · 2026-04-08 18:28:30

173

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Zeta function ratio

Published on 08 Apr 2026 - 18:28

score 299 · Answer 3 · 2021-02-23 22:10:21

299

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Is there an elegant exact formula for the zeta zero counting function?

Published on 23 Feb 2021 - 22:10

score 153 · Answer 4 · 2021-02-24 22:04:56

153

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Source for closed form of sum $\sum_{n=0}^\infty\zeta(2+2n)x^{2n}$

Published on 24 Feb 2021 - 22:04

score 108 · Answer 5 · 2026-04-10 18:20:03

108

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Analysis of series containing Zeta function:

Published on 10 Apr 2026 - 18:20

score 113 · Answer 6 · 2021-02-27 04:21:10

113

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Closed form for limit of a sum $\lim\limits_{m\to\infty}(\ln m-4\sum_{n=1}^{m}\frac{(-1)^{n}}{2n+1}\sum_{k=1}^{2n}(-1)^{k}k\ln k)\approx-0.092$

Published on 27 Feb 2021 - 4:21

score 69 · Answer 7 · 2026-03-27 02:40:29

69

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Prove$\sum_{|\alpha|<1, f(\alpha)=0}\log \frac{1}{|\alpha|}= \sum_{\Re(\rho)>1/2}\log\ |\frac{\rho}{1-\rho}|$

Published on 27 Mar 2026 - 2:40

score 106 · Answer 8 · 2026-04-09 15:34:34

106

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Trying to prove Trivial zeros of Zeta using Abel-Plana's formula

Published on 09 Apr 2026 - 15:34

score 236 · Answer 9 · 2026-03-27 02:40:27

236

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$f(z)=\frac{z}{1-z} \zeta(\frac {1}{1-z})$ belongs to Hardy Space $H^{1/3}(\mathbf{D})$

Published on 27 Mar 2026 - 2:40

score 93 · Answer 10 · 2026-04-11 10:43:09

93

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Questions on evaluation of $\frac{\zeta'(s)}{\zeta(s)}$ at integer values of s

Published on 11 Apr 2026 - 10:43

score 78 · Answer 11 · 2026-03-27 13:27:23

78

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Proof of Vaughan's identity, based on comparing the Dirichlet coefficients

Published on 27 Mar 2026 - 13:27

score 66 · Answer 12 · 2021-03-05 18:01:44

66

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$f(z)= (s-1) \zeta(s)$. Prove that $\log |f(0)|=0$

Published on 05 Mar 2021 - 18:01

score 347 · Answer 13 · 2026-03-27 02:36:07

347

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$\int_{-\infty}^{\infty} \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ where $\zeta$ is the Riemann zeta function

Published on 27 Mar 2026 - 2:36

score 155 · Answer 14 · 2026-03-26 14:35:00

155

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Prove that the infinite sum of the difference of even and odd values of the Riemann zeta function is 1/2

Published on 26 Mar 2026 - 14:35

score 126 · Answer 15 · 2026-04-09 22:07:13

126

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The Zeta Function and the Prime Number Theorem

Published on 09 Apr 2026 - 22:07

List Question

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Zeta function ratio

Is there an elegant exact formula for the zeta zero counting function?

Source for closed form of sum $\sum_{n=0}^\infty\zeta(2+2n)x^{2n}$

Analysis of series containing Zeta function:

Closed form for limit of a sum $\lim\limits_{m\to\infty}(\ln m-4\sum_{n=1}^{m}\frac{(-1)^{n}}{2n+1}\sum_{k=1}^{2n}(-1)^{k}k\ln k)\approx-0.092$

Prove$\sum_{|\alpha|<1, f(\alpha)=0}\log \frac{1}{|\alpha|}= \sum_{\Re(\rho)>1/2}\log\ |\frac{\rho}{1-\rho}|$

Trying to prove Trivial zeros of Zeta using Abel-Plana's formula

$f(z)=\frac{z}{1-z} \zeta(\frac {1}{1-z})$ belongs to Hardy Space $H^{1/3}(\mathbf{D})$

Questions on evaluation of $\frac{\zeta'(s)}{\zeta(s)}$ at integer values of s

Proof of Vaughan's identity, based on comparing the Dirichlet coefficients

$f(z)= (s-1) \zeta(s)$. Prove that $\log |f(0)|=0$

$\int_{-\infty}^{\infty} \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ where $\zeta$ is the Riemann zeta function

Prove that the infinite sum of the difference of even and odd values of the Riemann zeta function is 1/2

The Zeta Function and the Prime Number Theorem

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