Question

Moving the integral $Q(x) = -\frac{e^{-1/2x}}{4i}\int_{1/2-i\infty}^{1/2+i\infty} \zeta(s)\Gamma(\frac{s}{2})\pi^{-s/2}e^{xs} ds$ past Re(s) = 1.

score 164 · Answer 1 · 2015-01-23 23:19:27

164

Views

Moving the integral $Q(x) = -\frac{e^{-1/2x}}{4i}\int_{1/2-i\infty}^{1/2+i\infty} \zeta(s)\Gamma(\frac{s}{2})\pi^{-s/2}e^{xs} ds$ past Re(s) = 1.

Published on 23 Jan 2015 - 23:19

score 232 · Answer 2 · 2015-02-10 11:42:27

232

Views

Generating function for the zeta function

Published on 10 Feb 2015 - 11:42

score 1.2k · Answer 3 · 2015-02-21 22:59:27

1.2k

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Convergence of the series for the Dedekind zeta function

Published on 21 Feb 2015 - 22:59

score 292 · Answer 4 · 2015-02-22 19:40:33

292

Views

Proving $\zeta(2) - \beta(1) + \zeta(4) - \beta(3) + \zeta(6)- \beta(5) + \ldots=1$

Published on 22 Feb 2015 - 19:40

score 247 · Answer 5 · 2015-03-10 09:36:49

247

Views

Why the equality of spectral zeta functions imply the isospectrality?

Published on 10 Mar 2015 - 9:36

score 54 · Answer 6 · 2015-03-10 15:19:45

54

Views

Divergence Dedekind zeta function

Published on 10 Mar 2015 - 15:19

score 431 · Answer 7 · 2015-03-15 10:30:51

431

Views

What special role plays the function $\pi^{\frac x\pi}$ in analysis?

Published on 15 Mar 2015 - 10:30

score 105 · Answer 8 · 2026-03-25 16:08:20

105

Views

zeta function of abelian varieties and the exterior algebra

Published on 25 Mar 2026 - 16:08

score 595 · Answer 9 · 2015-03-29 12:59:09

zeta-function regularization $\prod_{m,n\in \mathbf{Z}}(m+n\tau+u)=iy^{\frac{1}{2}} q^{\frac{1}{12}} \prod_{n=1}^{\infty} (1-yq^n)(1-y^{-1}q^{n-1})$

score 543 · Answer 10 · 2015-04-10 07:19:19

543

Views

Any possible suspects for $\zeta(3)$?

Published on 10 Apr 2015 - 7:19

score 176 · Answer 11 · 2015-04-20 10:43:59

176

Views

Generating function for the Hurwitz Zeta: $\sum_{k=1}^{\infty}\zeta_{H}(k+1,a)(-z)^{k}$

Published on 20 Apr 2015 - 10:43

score 300 · Answer 12 · 2015-04-20 16:43:40

300

Views

$\sum\limits _{n=1}^{\infty}\frac{1}{n^s}=50$ Riemann-Zeta

Published on 20 Apr 2015 - 16:43

score 50 · Answer 13 · 2026-03-26 07:33:53

50

Views

Zeta Function : Identify This Variant of an $L $- Series

Published on 26 Mar 2026 - 7:33

score 281 · Answer 14 · 2026-03-25 06:26:25

281

Views

Summation of a function

Published on 25 Mar 2026 - 6:26

score 72 · Answer 15 · 2026-03-25 12:47:30

72

Views

Kronecker Zeta function

Published on 25 Mar 2026 - 12:47

List Question

Moving the integral $Q(x) = -\frac{e^{-1/2x}}{4i}\int_{1/2-i\infty}^{1/2+i\infty} \zeta(s)\Gamma(\frac{s}{2})\pi^{-s/2}e^{xs} ds$ past Re(s) = 1.

Generating function for the zeta function

Convergence of the series for the Dedekind zeta function

Proving $\zeta(2) - \beta(1) + \zeta(4) - \beta(3) + \zeta(6)- \beta(5) + \ldots=1$

Why the equality of spectral zeta functions imply the isospectrality?

Divergence Dedekind zeta function

What special role plays the function $\pi^{\frac x\pi}$ in analysis?

zeta function of abelian varieties and the exterior algebra

zeta-function regularization $\prod_{m,n\in \mathbf{Z}}(m+n\tau+u)=iy^{\frac{1}{2}} q^{\frac{1}{12}} \prod_{n=1}^{\infty} (1-yq^n)(1-y^{-1}q^{n-1})$

Any possible suspects for $\zeta(3)$?

Generating function for the Hurwitz Zeta: $\sum_{k=1}^{\infty}\zeta_{H}(k+1,a)(-z)^{k}$

$\sum\limits _{n=1}^{\infty}\frac{1}{n^s}=50$ Riemann-Zeta

Zeta Function : Identify This Variant of an $L $- Series

Summation of a function

Kronecker Zeta function

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