Question

Is this expression of the Riemann zeta function as a Mellin transform true for $\Im\{s\}\neq 0$?

score 104 · Answer 1 · 2018-06-27 21:35:33

104

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Is this expression of the Riemann zeta function as a Mellin transform true for $\Im\{s\}\neq 0$?

Published on 27 Jun 2018 - 21:35

score 205 · Answer 2 · 2018-08-23 11:27:59

205

Views

Mellin transform - change of variables in double integral

Published on 23 Aug 2018 - 11:27

score 245 · Answer 3 · 2026-03-24 22:09:29

245

Views

"Bilateral Mellin convolution"

Published on 24 Mar 2026 - 22:09

score 174 · Answer 4 · 2026-03-25 03:02:16

174

Views

isometry relating $L^2(\mathbb{R}, dx)$ and $L^2([0, \infty), \frac{dx}{x})$

Published on 25 Mar 2026 - 3:02

score 226 · Answer 5 · 2018-10-24 00:57:02

226

Views

What is the convergence of the explicit formula for $\frac{\zeta'(s)}{\zeta(s)}$?

Published on 24 Oct 2018 - 0:57

score 230 · Answer 6 · 2026-03-25 03:03:18

230

Views

Questions related to $f(x)$ where the Riemann Xi function $\xi(s)=s\int_0^\infty f(x)\,x^{-s-1}\,dx$

Published on 25 Mar 2026 - 3:03

score 231 · Answer 7 · 2018-11-16 02:05:33

231

Views

Questions related to the Riemann Xi function $\xi(s)$ and Jacobi theta functions $\vartheta_3(0,q)$

Published on 16 Nov 2018 - 2:05

score 181 · Answer 8 · 2026-03-20 03:58:47

181

Views

Uniqueness of $L$-series of cusp forms

Published on 20 Mar 2026 - 3:58

score 137 · Answer 9 · 2026-03-22 13:08:22

137

Views

Polynomial growth of L-function

Published on 22 Mar 2026 - 13:08

score 208 · Answer 10 · 2026-03-24 22:09:49

208

Views

Fourier and Mellin transforms of Hilbert Transform

Published on 24 Mar 2026 - 22:09

score 346 · Answer 11 · 2026-03-22 17:11:19

346

Views

What is the Explicit Formula for $\log(\zeta(s))$?

Published on 22 Mar 2026 - 17:11

score 85 · Answer 12 · 2018-12-19 21:49:22

85

Views

Methods on finding closed form of $\int_0^\infty x^{s-1}e^{-a(x+\frac{1}{x})}dx$

Published on 19 Dec 2018 - 21:49

score 302 · Answer 13 · 2019-01-10 17:19:43

302

Views

What is the relationship between simple prime-power counting function and $\log\zeta(s)$?

Published on 10 Jan 2019 - 17:19

score 200 · Answer 14 · 2019-01-14 21:43:22

200

Views

Questions related to the Dirichlet series for $\frac{\zeta'(s)}{\zeta(s)^2}$

Published on 14 Jan 2019 - 21:43

score 136 · Answer 15 · 2019-01-23 00:14:58

136

Views

Is there a preference if one of the functions in convolution of Mellin transform is divergent?

Published on 23 Jan 2019 - 0:14

List Question

Is this expression of the Riemann zeta function as a Mellin transform true for $\Im\{s\}\neq 0$?

Mellin transform - change of variables in double integral

"Bilateral Mellin convolution"

isometry relating $L^2(\mathbb{R}, dx)$ and $L^2([0, \infty), \frac{dx}{x})$

What is the convergence of the explicit formula for $\frac{\zeta'(s)}{\zeta(s)}$?

Questions related to $f(x)$ where the Riemann Xi function $\xi(s)=s\int_0^\infty f(x)\,x^{-s-1}\,dx$

Questions related to the Riemann Xi function $\xi(s)$ and Jacobi theta functions $\vartheta_3(0,q)$

Uniqueness of $L$-series of cusp forms

Polynomial growth of L-function

Fourier and Mellin transforms of Hilbert Transform

What is the Explicit Formula for $\log(\zeta(s))$?

Methods on finding closed form of $\int_0^\infty x^{s-1}e^{-a(x+\frac{1}{x})}dx$

What is the relationship between simple prime-power counting function and $\log\zeta(s)$?

Questions related to the Dirichlet series for $\frac{\zeta'(s)}{\zeta(s)^2}$

Is there a preference if one of the functions in convolution of Mellin transform is divergent?

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