Question

Is known the function $\sum_{n=1}^\infty\frac{(-1)^n\mu(n)}{n^s}$, where $s$ is the complex variable and $\mu(n)$ the Möbius function?

score 152 · Answer 1 · 2017-12-27 10:25:02

152

Views

Is known the function $\sum_{n=1}^\infty\frac{(-1)^n\mu(n)}{n^s}$, where $s$ is the complex variable and $\mu(n)$ the Möbius function?

Published on 27 Dec 2017 - 10:25

score 48 · Answer 2 · 2026-03-26 06:04:13

48

Views

Closed forms at integer values for Euler products with Dirichlet $\chi_{4}(p^s)$. Could these be extended towards non-integer values?

Published on 26 Mar 2026 - 6:04

score 140 · Answer 3 · 2017-12-31 12:04:02

140

Views

How to prove $L(s, \chi_0 \chi^) = 0$ if and only if $L(s, \chi^) = 0$?

Published on 31 Dec 2017 - 12:04

score 77 · Answer 4 · 2018-01-03 13:07:54

77

Views

What about the convergence of $\lim_{x\to\infty}\sum_{1\leq n\leq x}\frac{\lambda(n)}{\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$?

Published on 03 Jan 2018 - 13:07

score 56 · Answer 5 · 2018-01-06 06:04:30

56

Views

Convergence of product of series to zeta function

Published on 06 Jan 2018 - 6:04

score 479 · Answer 6 · 2018-01-06 20:13:06

479

Views

Convergence of Series $\sum_{n=1}^{\infty} \left[ \frac{\sin \left( \frac{n^2+1}{n}x\right)}{\sqrt{n}}\left( 1+\frac{1}{n}\right)^n\right]$

Published on 06 Jan 2018 - 20:13

score 99 · Answer 7 · 2018-01-08 17:59:48

99

Views

Prove that this type of alternating series admits this supremum.

Published on 08 Jan 2018 - 17:59

score 2.3k · Answer 8 · 2010-12-23 16:41:02

2.3k

Views

On Dirichlet series and critical strips

Published on 23 Dec 2010 - 16:41

score 901 · Answer 9 · 2011-10-17 14:45:59

901

Views

Two Dirichlet's series related to the Divisor Summatory Function and to the Riemann's zeta-function, $\zeta(s)$

Published on 17 Oct 2011 - 14:45

score 253 · Answer 10 · 2011-11-05 03:17:46

253

Views

A question about an identity involving Dirichlet characters

Published on 05 Nov 2011 - 3:17

score 971 · Answer 11 · 2011-11-06 04:06:06

971

Views

Reference request: $L$-series and $\zeta$-functions

Published on 06 Nov 2011 - 4:06

score 2.3k · Answer 12 · 2011-11-20 01:47:19

2.3k

Views

An identity involving the Möbius function

Published on 20 Nov 2011 - 1:47

score 1.3k · Answer 13 · 2026-03-26 12:50:39

1.3k

Views

How to simplify $\newcommand{\bigk}{\mathop{\vcenter{\hbox{K}}}}\prod_{p\in\mathbb{P}}\left(1+\bigk_{k=1}^{\infty }\frac{f_k(s)}{g_k(s)}\right)^{-1}$

Published on 26 Mar 2026 - 12:50

score 274 · Answer 14 · 2011-12-01 05:15:21

274

Views

Convergence of sum in proof that $\Phi(s) - \frac{1}{s-1}$ extends to $\Re(s) > \frac{1}{2}$

Published on 01 Dec 2011 - 5:15

score 897 · Answer 15 · 2011-12-02 22:19:56

897

Views

Approximate Riemann zeta function

Published on 02 Dec 2011 - 22:19

List Question

Is known the function $\sum_{n=1}^\infty\frac{(-1)^n\mu(n)}{n^s}$, where $s$ is the complex variable and $\mu(n)$ the Möbius function?

Closed forms at integer values for Euler products with Dirichlet $\chi_{4}(p^s)$. Could these be extended towards non-integer values?

How to prove $L(s, \chi_0 \chi^) = 0$ if and only if $L(s, \chi^) = 0$?

What about the convergence of $\lim_{x\to\infty}\sum_{1\leq n\leq x}\frac{\lambda(n)}{\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$?

Convergence of product of series to zeta function

Convergence of Series $\sum_{n=1}^{\infty} \left[ \frac{\sin \left( \frac{n^2+1}{n}x\right)}{\sqrt{n}}\left( 1+\frac{1}{n}\right)^n\right]$

Prove that this type of alternating series admits this supremum.

On Dirichlet series and critical strips

Two Dirichlet's series related to the Divisor Summatory Function and to the Riemann's zeta-function, $\zeta(s)$

A question about an identity involving Dirichlet characters

Reference request: $L$-series and $\zeta$-functions

An identity involving the Möbius function

How to simplify $\newcommand{\bigk}{\mathop{\vcenter{\hbox{K}}}}\prod_{p\in\mathbb{P}}\left(1+\bigk_{k=1}^{\infty }\frac{f_k(s)}{g_k(s)}\right)^{-1}$

Convergence of sum in proof that $\Phi(s) - \frac{1}{s-1}$ extends to $\Re(s) > \frac{1}{2}$

Approximate Riemann zeta function

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