Question

What is the Dirichlet Transform of $a(n)=\frac{\mu(n)}{n^2}\,\log\left(\frac{2\,\pi}{n}\right)$?

score 150 · Answer 1 · 2026-03-25 07:44:38

150

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What is the Dirichlet Transform of $a(n)=\frac{\mu(n)}{n^2}\,\log\left(\frac{2\,\pi}{n}\right)$?

Published on 25 Mar 2026 - 7:44

score 150 · Answer 2 · 2019-03-20 03:38:26

150

Views

Closed form solution for $\int_0^1 \frac{\ln^2(x)\ln^2(1-x)}{x(1-x)} dx$ using Bose Integral

Published on 20 Mar 2019 - 3:38

score 133 · Answer 3 · 2026-03-25 07:58:46

133

Views

Need reference for proof of functional equation for generalized L-functions

Published on 25 Mar 2026 - 7:58

score 48 · Answer 4 · 2026-03-25 12:21:12

48

Views

Is this $\zeta(p)=\sum_{k\geq1 ,p\in \mathbb{P}}\frac{1}{{\sigma}_k(p)-1}$ true with sigma is power of sum divisor function?

Published on 25 Mar 2026 - 12:21

score 244 · Answer 5 · 2026-03-25 09:29:07

244

Views

For what real part of $s$ as a function of $q$ is the Euler-Maclaurin formula a valid analytic continuation of the Riemann zeta function?

Published on 25 Mar 2026 - 9:29

score 237 · Answer 6 · 2019-03-26 11:08:12

237

Views

The use of limit in Titchmarsh's book "The theory of the Riemann zeta-function" in Theorem $3.13$

Published on 26 Mar 2019 - 11:08

score 258 · Answer 7 · 2026-03-28 16:04:10

258

Views

Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$

Published on 28 Mar 2026 - 16:04

score 1.5k · Answer 8 · 2019-03-27 08:12:12

1.5k

Views

A series related to prime numbers

Published on 27 Mar 2019 - 8:12

score 222 · Answer 9 · 2026-03-25 19:10:20

222

Views

What is $\zeta(i \infty )$ if $ \zeta(\infty)=1 $ and what is its geometric interpretation?

Published on 25 Mar 2026 - 19:10

score 74 · Answer 10 · 2019-03-28 12:28:07

74

Views

evaluating a double integer series

Published on 28 Mar 2019 - 12:28

score 80 · Answer 11 · 2019-03-28 23:36:30

80

Views

Summation of Integrals without using $\zeta(2)$

Published on 28 Mar 2019 - 23:36

score 52 · Answer 12 · 2019-04-03 13:36:33

52

Views

Sum of almost-prime zeta functions. Part II

Published on 03 Apr 2019 - 13:36

score 195 · Answer 13 · 2019-04-04 18:38:50

195

Views

Ratio of $\zeta(s)$ and $\zeta(1-s)$ in the functional equation

Published on 04 Apr 2019 - 18:38

score 42 · Answer 14 · 2026-03-27 00:58:35

42

Views

How can i prove the following Infinite Product?

Published on 27 Mar 2026 - 0:58

score 2.1k · Answer 15 · 2026-03-25 11:08:14

2.1k

Views

Binomial expansion with gamma function

Published on 25 Mar 2026 - 11:08

List Question

What is the Dirichlet Transform of $a(n)=\frac{\mu(n)}{n^2}\,\log\left(\frac{2\,\pi}{n}\right)$?

Closed form solution for $\int_0^1 \frac{\ln^2(x)\ln^2(1-x)}{x(1-x)} dx$ using Bose Integral

Need reference for proof of functional equation for generalized L-functions

Is this $\zeta(p)=\sum_{k\geq1 ,p\in \mathbb{P}}\frac{1}{{\sigma}_k(p)-1}$ true with sigma is power of sum divisor function?

For what real part of $s$ as a function of $q$ is the Euler-Maclaurin formula a valid analytic continuation of the Riemann zeta function?

The use of limit in Titchmarsh's book "The theory of the Riemann zeta-function" in Theorem $3.13$

Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$

A series related to prime numbers

What is $\zeta(i \infty )$ if $ \zeta(\infty)=1 $ and what is its geometric interpretation?

evaluating a double integer series

Summation of Integrals without using $\zeta(2)$

Sum of almost-prime zeta functions. Part II

Ratio of $\zeta(s)$ and $\zeta(1-s)$ in the functional equation

How can i prove the following Infinite Product?

Binomial expansion with gamma function

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