Question

Show that $\int_0^1 4 \space\operatorname{li}(x)^3 \space (x-1) \space x^{-3} dx = \zeta(3) $

score 346 · Answer 1 · 2026-03-25 15:12:12

346

Views

Show that $\int_0^1 4 \space\operatorname{li}(x)^3 \space (x-1) \space x^{-3} dx = \zeta(3) $

Published on 25 Mar 2026 - 15:12

score 101 · Answer 2 · 2026-03-25 06:12:44

101

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Prime gaps and gaps between successive critical zeros of zeta

Published on 25 Mar 2026 - 6:12

score 77 · Answer 3 · 2018-07-31 19:27:47

77

Views

Calculating the symbolic solution to a definite integral containing trigonometric functions

Published on 31 Jul 2018 - 19:27

score 872 · Answer 4 · 2026-03-25 06:00:07

872

Views

Motivation for the Basel problem

Published on 25 Mar 2026 - 6:00

score 180 · Answer 5 · 2026-03-25 21:54:07

180

Views

Is there another way of evaluating $\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x))=\frac{\pi^2}{6}$

Published on 25 Mar 2026 - 21:54

score 376 · Answer 6 · 2026-03-25 03:04:16

376

Views

What is $f(2s+1)$ when $f(s)=\sum_{n=0}^\infty {\frac{(-1)^n}{(2n+1)^s}}=1-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\dots$?

Published on 25 Mar 2026 - 3:04

score 140 · Answer 7 · 2026-03-25 03:07:30

140

Views

Is there a zeta function(with a Dirichlet series) having known roots off the critical line?

Published on 25 Mar 2026 - 3:07

score 734 · Answer 8 · 2026-03-25 04:42:56

734

Views

Mathematical Explanation of Mathematica Summation ${\sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)}$

Published on 25 Mar 2026 - 4:42

score 132 · Answer 9 · 2026-03-25 12:49:07

132

Views

Notation: What does "$p-1|n$" mean in "$\prod_{p-1|n} p$"?

Published on 25 Mar 2026 - 12:49

score 134 · Answer 10 · 2018-08-16 09:23:32

134

Views

How is this equation obtained? $\int_0^\infty \frac{x^{s-1} dx}{e^x-1}=\Pi(s-1)\zeta(s) $

Published on 16 Aug 2018 - 9:23

score 340 · Answer 11 · 2026-03-24 20:33:23

340

Views

Can we prove $B (n) = \frac{1}{4} G (n - 1) G (n)$ is an indicator function that takes on the value 1 for 'bad' and 0 for "good" Gram points?

Published on 24 Mar 2026 - 20:33

score 1.4k · Answer 12 · 2026-03-27 05:58:11

1.4k

Views

Calculating the first zero of Riemann Zeta Function by hand

Published on 27 Mar 2026 - 5:58

score 347 · Answer 13 · 2018-08-19 04:14:42

347

Views

Does a generating function for $\zeta(2k+1)$ exist?

Published on 19 Aug 2018 - 4:14

score 1k · Answer 14 · 2018-08-19 05:35:56

1k

Views

Does there exist positive rational $s$ for which $\zeta(s)$ is a positive integer?

Published on 19 Aug 2018 - 5:35

score 97 · Answer 15 · 2018-08-20 20:36:32

97

Views

Sum of products of $m$-tuples chosen from the set of squared reciprocals

Published on 20 Aug 2018 - 20:36

List Question

Show that $\int_0^1 4 \space\operatorname{li}(x)^3 \space (x-1) \space x^{-3} dx = \zeta(3) $

Prime gaps and gaps between successive critical zeros of zeta

Calculating the symbolic solution to a definite integral containing trigonometric functions

Motivation for the Basel problem

Is there another way of evaluating $\lim_{x \to 0} \Gamma(x)(\gamma+\psi(1+x))=\frac{\pi^2}{6}$

What is $f(2s+1)$ when $f(s)=\sum_{n=0}^\infty {\frac{(-1)^n}{(2n+1)^s}}=1-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\dots$?

Is there a zeta function(with a Dirichlet series) having known roots off the critical line?

Mathematical Explanation of Mathematica Summation ${\sum_{n=1}^{\infty}\frac{(2n-1)!}{(2n+2)!}\zeta(2n)}$

Notation: What does "$p-1|n$" mean in "$\prod_{p-1|n} p$"?

How is this equation obtained? $\int_0^\infty \frac{x^{s-1} dx}{e^x-1}=\Pi(s-1)\zeta(s) $

Can we prove $B (n) = \frac{1}{4} G (n - 1) G (n)$ is an indicator function that takes on the value 1 for 'bad' and 0 for "good" Gram points?

Calculating the first zero of Riemann Zeta Function by hand

Does a generating function for $\zeta(2k+1)$ exist?

Does there exist positive rational $s$ for which $\zeta(s)$ is a positive integer?

Sum of products of $m$-tuples chosen from the set of squared reciprocals

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