Question

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

score 345 · Answer 1 · 2026-05-07 10:09:17

345

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

Published on 07 May 2026 - 10:09

score 319 · Answer 2 · 2026-05-05 12:31:33

319

Views

Zeta regularization vs Dirichlet series

Published on 05 May 2026 - 12:31

score 187 · Answer 3 · 2026-04-29 12:34:36

187

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 29 Apr 2026 - 12:34

score 379 · Answer 4 · 2026-04-29 12:42:12

379

Views

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

Published on 29 Apr 2026 - 12:42

score 222 · Answer 5 · 2026-04-29 12:42:32

222

Views

Solving for variable inside a sum

Published on 29 Apr 2026 - 12:42

score 109 · Answer 6 · 2026-04-20 11:24:44

109

Views

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

Published on 20 Apr 2026 - 11:24

score 76 · Answer 7 · 2026-04-29 12:42:35

76

Views

Multiplicative arithmetic function on the unit disk

Published on 29 Apr 2026 - 12:42

score 422 · Answer 8 · 2026-05-10 10:11:18

422

Views

Question with Dirichlet convolution involving Mobius function and divisor function

Published on 10 May 2026 - 10:11

score 153 · Answer 9 · 2026-05-02 18:44:39

153

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 02 May 2026 - 18:44

score 137 · Answer 10 · 2026-05-02 18:28:07

137

Views

Dirichlet problem in terms of a Fourier sine series

Published on 02 May 2026 - 18:28

score 313 · Answer 11 · 2026-05-02 18:29:42

313

Views

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

Published on 02 May 2026 - 18:29

score 667 · Answer 12 · 2026-04-29 12:42:38

667

Views

Eisenstein series twisted by a Dirichlet character

Published on 29 Apr 2026 - 12:42

score 241 · Answer 13 · 2026-05-10 12:53:25

241

Views

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

Published on 10 May 2026 - 12:53

score 112 · Answer 14 · 2026-05-10 12:53:23

112

Views

Proof of McMahon's factorisatio numerorum result

Published on 10 May 2026 - 12:53

score 1.1k · Answer 15 · 2026-05-10 12:54:53

1.1k

Views

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

Published on 10 May 2026 - 12:54

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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