Question

On the integral $\int_1^\infty\big(\{x\}^n-\frac1{n+1}\big)\frac{dx}x$

score 245 · Answer 1 · 2018-07-12 11:01:21

245

Views

On the integral $\int_1^\infty\big(\{x\}^n-\frac1{n+1}\big)\frac{dx}x$

Published on 12 Jul 2018 - 11:01

score 116 · Answer 2 · 2018-07-13 02:28:25

116

Views

What's this $\sum_{n=2}^{+\infty}\frac{(-1)^n}{\zeta(n)}$ equal?

Published on 13 Jul 2018 - 2:28

score 98 · Answer 3 · 2018-07-13 18:37:21

98

Views

How can I show that :$\sum_{n=1}^{\infty}(-1)^{n-1}(\zeta(n+1)-1))=\frac12$?

Published on 13 Jul 2018 - 18:37

score 59 · Answer 4 · 2018-07-14 20:13:55

59

Views

Analytic Number Theory calculation involving zeta

Published on 14 Jul 2018 - 20:13

score 480 · Answer 5 · 2026-03-26 14:32:01

480

Views

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

Published on 26 Mar 2026 - 14:32

score 339 · Answer 6 · 2026-03-24 23:51:36

339

Views

The alternating series of square-free k-almost prime zeta functions converges to the reciprocal zeta?

Published on 24 Mar 2026 - 23:51

score 503 · Answer 7 · 2018-07-16 19:24:39

503

Views

Riemann Zeta function is Big Oh of log(|t|)

Published on 16 Jul 2018 - 19:24

score 267 · Answer 8 · 2026-03-25 01:22:39

267

Views

Fractional part of the floor function Integral

Published on 25 Mar 2026 - 1:22

score 191 · Answer 9 · 2026-03-25 01:18:15

191

Views

Does $N_0(T) =N(T)$ where $N$ is the exact Riemann $\zeta$ zero counting function and $N_0$ is the approximate zero counting function imply the RH?

Published on 25 Mar 2026 - 1:18

score 58 · Answer 10 · 2026-03-26 02:46:46

Is there a bounded function that is always greater than $M (t) = \max_{s \in [0, t]} \left| \zeta \left( \frac{1}{2} + i s \right) \right|$?

score 126 · Answer 11 · 2026-03-25 03:07:23

126

Views

Holomorphic but not a Dirichlet series

Published on 25 Mar 2026 - 3:07

score 707 · Answer 12 · 2018-07-25 16:05:23

707

Views

Sum over all inverse zeta nontrivial zeros

Published on 25 Jul 2018 - 16:05

score 183 · Answer 13 · 2026-03-25 06:11:05

183

Views

symmetric double-integral on fractional part

Published on 25 Mar 2026 - 6:11

score 214 · Answer 14 · 2026-03-25 03:00:24

214

Views

Imaginary component of Dirichlet Eta Function's root with real component equal to 1/2

Published on 25 Mar 2026 - 3:00

score 226 · Answer 15 · 2018-07-28 21:30:11

226

Views

What is the geometric interpretation of this limit :$\lim_{n\to {+\infty}}\zeta(n)+\zeta(\frac1n)=\frac12$?

Published on 28 Jul 2018 - 21:30

List Question

On the integral $\int_1^\infty\big(\{x\}^n-\frac1{n+1}\big)\frac{dx}x$

What's this $\sum_{n=2}^{+\infty}\frac{(-1)^n}{\zeta(n)}$ equal?

How can I show that :$\sum_{n=1}^{\infty}(-1)^{n-1}(\zeta(n+1)-1))=\frac12$?

Analytic Number Theory calculation involving zeta

Proof that $\sum\limits _{n=1}^{\infty } n\sum\limits _{j=2}^{\infty }{\frac {(-1)^{j-1}}{j^2} \left( 1-{j}^{-1} \right)^{n-1}} = -\frac12$

The alternating series of square-free k-almost prime zeta functions converges to the reciprocal zeta?

Riemann Zeta function is Big Oh of log(|t|)

Fractional part of the floor function Integral

Does $N_0(T) =N(T)$ where $N$ is the exact Riemann $\zeta$ zero counting function and $N_0$ is the approximate zero counting function imply the RH?

Is there a bounded function that is always greater than $M (t) = \max_{s \in [0, t]} \left| \zeta \left( \frac{1}{2} + i s \right) \right|$?

Holomorphic but not a Dirichlet series

Sum over all inverse zeta nontrivial zeros

symmetric double-integral on fractional part

Imaginary component of Dirichlet Eta Function's root with real component equal to 1/2

What is the geometric interpretation of this limit :$\lim_{n\to {+\infty}}\zeta(n)+\zeta(\frac1n)=\frac12$?

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