Question

Generalization of a $\det$ series for $\zeta_{\mathbb{Q}(\zeta_k)}$

score 185 · Answer 1 · 2026-03-25 22:30:48

185

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Generalization of a $\det$ series for $\zeta_{\mathbb{Q}(\zeta_k)}$

Published on 25 Mar 2026 - 22:30

score 230 · Answer 2 · 2017-10-07 17:37:39

230

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Looking for the closed form of $\sum_{n=1}^{\infty}{\zeta(2n+1)\over (2n+1)2^{4n}}$

Published on 07 Oct 2017 - 17:37

score 227 · Answer 3 · 2017-10-12 03:48:31

227

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Summation to Integral

Published on 12 Oct 2017 - 3:48

score 824 · Answer 4 · 2017-10-12 23:14:44

824

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Show that $\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + 58 n^2} = - \frac{\pi \ln( 27 + 5 \sqrt {29})}{\sqrt {58}} $

Published on 12 Oct 2017 - 23:14

score 298 · Answer 5 · 2017-10-18 16:24:42

298

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What is the closed-form for $\displaystyle\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + mn+41n^2}$?

Published on 18 Oct 2017 - 16:24

score 58 · Answer 6 · 2017-10-20 09:05:46

58

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How can one (reasonably) interpret this equality between the divergent $\zeta(1)$ and a division by $0$?

Published on 20 Oct 2017 - 9:05

score 114 · Answer 7 · 2017-10-22 15:34:51

114

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Zeta function over a finitely generated commutative ring 2

Published on 22 Oct 2017 - 15:34

score 435 · Answer 8 · 2017-10-23 01:53:49

435

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Mistake while computing residue of Dedekind Zeta function

Published on 23 Oct 2017 - 1:53

score 190 · Answer 9 · 2017-10-31 03:13:09

190

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Numerical evaluation of zeta function $\zeta(-1)=1+2+3+\cdots= -1/12$

Published on 31 Oct 2017 - 3:13

score 465 · Answer 10 · 2017-11-02 16:53:35

465

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Show that $\zeta_K(2) = \frac{\pi^4}{48 \sqrt{2}} $, with $K = \mathbb{Q}(\sqrt{2})$

Published on 02 Nov 2017 - 16:53

score 162 · Answer 11 · 2017-11-03 01:59:50

162

Views

Random Walks and the Locus of Partial Sums of the Riemann Zeta Function

Published on 03 Nov 2017 - 1:59

score 104 · Answer 12 · 2017-11-16 14:39:21

104

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Showing that the zeta function does not vanish on $Re(z)=1$

Published on 16 Nov 2017 - 14:39

score 151 · Answer 13 · 2017-11-23 16:33:30

151

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Show that $\zeta(2,2) = \frac{3}{4} \zeta(4)$ by integrating $\int \frac{dx}{x} \wedge \frac{dx}{x} \wedge \frac{dx}{1-x} \wedge \frac{dx}{1-x}$

Published on 23 Nov 2017 - 16:33

score 163 · Answer 14 · 2017-12-03 19:20:38

163

Views

Question about series involving zeta function

Published on 03 Dec 2017 - 19:20

score 72 · Answer 15 · 2026-03-26 11:07:07

72

Views

How to regularize $\sum_{(a,b) \in \mathbb{Z}^2}' \frac{1}{\sqrt{a^2 + b^2}} $?

Published on 26 Mar 2026 - 11:07

List Question

Generalization of a $\det$ series for $\zeta_{\mathbb{Q}(\zeta_k)}$

Looking for the closed form of $\sum_{n=1}^{\infty}{\zeta(2n+1)\over (2n+1)2^{4n}}$

Summation to Integral

Show that $\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + 58 n^2} = - \frac{\pi \ln( 27 + 5 \sqrt {29})}{\sqrt {58}} $

What is the closed-form for $\displaystyle\sum_{m,n = - \infty}^{\infty} \frac{(-1)^m}{m^2 + mn+41n^2}$?

How can one (reasonably) interpret this equality between the divergent $\zeta(1)$ and a division by $0$?

Zeta function over a finitely generated commutative ring 2

Mistake while computing residue of Dedekind Zeta function

Numerical evaluation of zeta function $\zeta(-1)=1+2+3+\cdots= -1/12$

Show that $\zeta_K(2) = \frac{\pi^4}{48 \sqrt{2}} $, with $K = \mathbb{Q}(\sqrt{2})$

Random Walks and the Locus of Partial Sums of the Riemann Zeta Function

Showing that the zeta function does not vanish on $Re(z)=1$

Show that $\zeta(2,2) = \frac{3}{4} \zeta(4)$ by integrating $\int \frac{dx}{x} \wedge \frac{dx}{x} \wedge \frac{dx}{1-x} \wedge \frac{dx}{1-x}$

Question about series involving zeta function

How to regularize $\sum_{(a,b) \in \mathbb{Z}^2}' \frac{1}{\sqrt{a^2 + b^2}} $?

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