Question

Is this Dirichlet "$\eta$ version" of the inverse relationship between $\zeta(s)$ and the Möbius function correct?

score 471 · Answer 1 · 2017-01-10 20:44:17

471

Views

Is this Dirichlet "$\eta$ version" of the inverse relationship between $\zeta(s)$ and the Möbius function correct?

Published on 10 Jan 2017 - 20:44

score 2.2k · Answer 2 · 2026-03-25 13:23:24

2.2k

Views

Using Dirichlet's test

Published on 25 Mar 2026 - 13:23

score 33 · Answer 3 · 2017-02-07 21:16:59

33

Views

Continuous transformation of a q-expansion into a Dirichlet series

Published on 07 Feb 2017 - 21:16

score 77 · Answer 4 · 2017-02-19 10:39:21

77

Views

Multiplicative coefficients of Selberg functions

Published on 19 Feb 2017 - 10:39

score 140 · Answer 5 · 2017-02-22 13:38:10

140

Views

The Parseval theorem applied to 8 well known functions. Could this be extended to L-series?

Published on 22 Feb 2017 - 13:38

score 479 · Answer 6 · 2017-03-03 21:08:41

479

Views

Computing the Dirichlet Density

Published on 03 Mar 2017 - 21:08

score 346 · Answer 7 · 2017-03-03 23:31:49

346

Views

Dirichlet density of $p \equiv 1 \bmod 8$

Published on 03 Mar 2017 - 23:31

score 75 · Answer 8 · 2017-03-04 19:21:15

75

Views

Is there a known example of a Dirichlet L series having at least one multiple root?

Published on 04 Mar 2017 - 19:21

score 82 · Answer 9 · 2017-03-12 11:22:09

82

Views

Taking the derivative inside the integral sign of Jensen or Lindelöf's integral representations related to the alternating Zeta function

Published on 12 Mar 2017 - 11:22

score 185 · Answer 10 · 2017-03-14 01:17:30

185

Views

Where does this series converge $\sum_{n=1}^\infty\frac{(-1)^{\mu(n)}}{n^s}$, being $\mu(n)$ the Möbius function?

Published on 14 Mar 2017 - 1:17

score 1.9k · Answer 11 · 2017-03-15 21:00:11

1.9k

Views

Proving convergence of the Dirichlet Eta function

Published on 15 Mar 2017 - 21:00

score 65 · Answer 12 · 2026-03-25 15:42:33

65

Views

On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Published on 25 Mar 2026 - 15:42

score 171 · Answer 13 · 2017-04-05 18:21:41

171

Views

Usage of the Dirichlet kernel in a trigonometric series proof

Published on 05 Apr 2017 - 18:21

score 139 · Answer 14 · 2026-03-25 15:41:22

139

Views

what is the name of this formula ? with mellin transform

Published on 25 Mar 2026 - 15:41

score 79 · Answer 15 · 2023-02-02 01:25:15

79

Views

Convergence of sums in $\ell^p \implies \ell^{p-\epsilon}$

Published on 02 Feb 2023 - 1:25

List Question

Is this Dirichlet "$\eta$ version" of the inverse relationship between $\zeta(s)$ and the Möbius function correct?

Using Dirichlet's test

Continuous transformation of a q-expansion into a Dirichlet series

Multiplicative coefficients of Selberg functions

The Parseval theorem applied to 8 well known functions. Could this be extended to L-series?

Computing the Dirichlet Density

Dirichlet density of $p \equiv 1 \bmod 8$

Is there a known example of a Dirichlet L series having at least one multiple root?

Taking the derivative inside the integral sign of Jensen or Lindelöf's integral representations related to the alternating Zeta function

Where does this series converge $\sum_{n=1}^\infty\frac{(-1)^{\mu(n)}}{n^s}$, being $\mu(n)$ the Möbius function?

Proving convergence of the Dirichlet Eta function

On $\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\eta'(s)\frac{x^s}{s\zeta(s)}ds$, for $c>1$, where $\eta(s)$ is the Dirichlet Eta function

Usage of the Dirichlet kernel in a trigonometric series proof

what is the name of this formula ? with mellin transform

Convergence of sums in $\ell^p \implies \ell^{p-\epsilon}$

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