Question

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

score 110 · Answer 1 · 2026-04-29 12:50:27

110

Views

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

Published on 29 Apr 2026 - 12:50

score 209 · Answer 2 · 2026-04-29 12:49:41

209

Views

Mellin transform - change of variables in double integral

Published on 29 Apr 2026 - 12:49

score 250 · Answer 3 · 2026-04-29 12:50:13

250

Views

"Bilateral Mellin convolution"

Published on 29 Apr 2026 - 12:50

score 177 · Answer 4 · 2026-04-29 12:49:41

177

Views

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

Published on 29 Apr 2026 - 12:49

score 231 · Answer 5 · 2026-04-29 12:50:23

231

Views

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

Published on 29 Apr 2026 - 12:50

score 231 · Answer 6 · 2026-04-29 12:49:49

231

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 29 Apr 2026 - 12:49

score 234 · Answer 7 · 2026-04-29 12:50:24

234

Views

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

Published on 29 Apr 2026 - 12:50

score 189 · Answer 8 · 2026-05-10 11:42:08

189

Views

Uniqueness of $L$-series of cusp forms

Published on 10 May 2026 - 11:42

score 140 · Answer 9 · 2026-04-29 12:50:29

140

Views

Polynomial growth of L-function

Published on 29 Apr 2026 - 12:50

score 210 · Answer 10 · 2026-04-29 12:50:12

210

Views

Fourier and Mellin transforms of Hilbert Transform

Published on 29 Apr 2026 - 12:50

score 348 · Answer 11 · 2026-04-29 12:49:47

348

Views

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

Published on 29 Apr 2026 - 12:49

score 88 · Answer 12 · 2026-04-29 12:50:13

88

Views

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

Published on 29 Apr 2026 - 12:50

score 305 · Answer 13 · 2026-04-29 12:50:21

305

Views

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

Published on 29 Apr 2026 - 12:50

score 202 · Answer 14 · 2026-04-29 12:49:52

202

Views

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

Published on 29 Apr 2026 - 12:49

score 138 · Answer 15 · 2026-04-29 12:49:43

138

Views

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

Published on 29 Apr 2026 - 12:49

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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