Question

Convergence of $\sum_{n=1}^{\infty}\frac{\mu(n)\chi(n)}{n^s}$ on $\Re{s}=1$

score 334 · Answer 1 · 2026-03-24 03:50:54

334

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Convergence of $\sum_{n=1}^{\infty}\frac{\mu(n)\chi(n)}{n^s}$ on $\Re{s}=1$

Published on 24 Mar 2026 - 3:50

score 309 · Answer 2 · 2026-03-23 04:01:33

309

Views

Zeta regularization vs Dirichlet series

Published on 23 Mar 2026 - 4:01

score 174 · Answer 3 · 2026-03-20 04:55:18

174

Views

A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

Published on 20 Mar 2026 - 4:55

score 371 · Answer 4 · 2026-03-20 08:25:36

371

Views

Dirichlet series, abscissa of absolute convergence $\neq$ abscissa of uniform convergence

Published on 20 Mar 2026 - 8:25

score 213 · Answer 5 · 2026-03-20 19:54:07

213

Views

Solving for variable inside a sum

Published on 20 Mar 2026 - 19:54

score 103 · Answer 6 · 2026-03-20 07:16:50

103

Views

Is $\sum_{n=0}^\infty (-1)^n (2n+1)^{-s}$ expressible in terms of the zeta function?

Published on 20 Mar 2026 - 7:16

score 68 · Answer 7 · 2026-03-20 05:41:05

68

Views

Multiplicative arithmetic function on the unit disk

Published on 20 Mar 2026 - 5:41

score 414 · Answer 8 · 2026-03-22 12:22:41

414

Views

Question with Dirichlet convolution involving Mobius function and divisor function

Published on 22 Mar 2026 - 12:22

score 145 · Answer 9 · 2026-03-20 03:18:03

145

Views

Question on Proof of the Equivalence of two Coefficient Functions Related to the Dirichlet Series for $\frac{\zeta(s+1)}{\zeta(s)}$

Published on 20 Mar 2026 - 3:18

score 128 · Answer 10 · 2026-03-20 06:52:48

128

Views

Dirichlet problem in terms of a Fourier sine series

Published on 20 Mar 2026 - 6:52

score 304 · Answer 11 · 2026-03-20 11:28:36

304

Views

Not-too-slow computation of Euler products / singular series

Published on 20 Mar 2026 - 11:28

score 660 · Answer 12 · 2026-03-23 15:39:50

660

Views

Eisenstein series twisted by a Dirichlet character

Published on 23 Mar 2026 - 15:39

score 233 · Answer 13 · 2026-03-22 23:41:41

233

Views

What is the explicit formula for $\Phi(x)=\sum\limits_{n=1}^x\phi(n)$?

Published on 22 Mar 2026 - 23:41

score 107 · Answer 14 · 2026-03-23 13:17:27

107

Views

Proof of McMahon's factorisatio numerorum result

Published on 23 Mar 2026 - 13:17

score 1.1k · Answer 15 · 2026-03-23 05:12:13

1.1k

Views

Dirichlet Series of Absolute value of Mobius Function equals Ratio of Riemann Zeta

Published on 23 Mar 2026 - 5:12

List Question

Convergence of $\sum_{n=1}^{\infty}\frac{\mu(n)\chi(n)}{n^s}$ on $\Re{s}=1$

Zeta regularization vs Dirichlet series

A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

Dirichlet series, abscissa of absolute convergence $\neq$ abscissa of uniform convergence

Solving for variable inside a sum

Is $\sum_{n=0}^\infty (-1)^n (2n+1)^{-s}$ expressible in terms of the zeta function?

Multiplicative arithmetic function on the unit disk

Question with Dirichlet convolution involving Mobius function and divisor function

Question on Proof of the Equivalence of two Coefficient Functions Related to the Dirichlet Series for $\frac{\zeta(s+1)}{\zeta(s)}$

Dirichlet problem in terms of a Fourier sine series

Not-too-slow computation of Euler products / singular series

Eisenstein series twisted by a Dirichlet character

What is the explicit formula for $\Phi(x)=\sum\limits_{n=1}^x\phi(n)$?

Proof of McMahon's factorisatio numerorum result

Dirichlet Series of Absolute value of Mobius Function equals Ratio of Riemann Zeta

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