Question

Is $\sum_{n=1}^\infty \ln \left(1-\frac{1}{p_n^s} \right)=-\ln \zeta(s)$ the only known series with primes and nontrivial closed form?

score 163 · Answer 1 · 2026-04-01 03:07:00

163

Views

Is $\sum_{n=1}^\infty \ln \left(1-\frac{1}{p_n^s} \right)=-\ln \zeta(s)$ the only known series with primes and nontrivial closed form?

Published on 01 Apr 2026 - 3:07

score 185 · Answer 2 · 2026-04-01 03:08:18

185

Views

Interesting connection between polylogarithms and polygamma functions.

Published on 01 Apr 2026 - 3:08

score 246 · Answer 3 · 2026-03-25 20:34:43

246

Views

Does Montgomery's pair correlation conjecture also hold true for Dedekind Zeta function ?

Published on 25 Mar 2026 - 20:34

score 122 · Answer 4 · 2026-03-25 11:15:53

122

Views

Relation between the derivative of hurwitz zeta and trigamma

Published on 25 Mar 2026 - 11:15

score 91 · Answer 5 · 2016-09-02 20:34:18

91

Views

What are some good introductory/elementary books on the Riemann zeta function?

Published on 02 Sep 2016 - 20:34

score 69 · Answer 6 · 2016-09-03 01:21:24

69

Views

Complex t in the Argument of the Zeta Function

Published on 03 Sep 2016 - 1:21

score 1.7k · Answer 7 · 2026-03-26 13:01:46

1.7k

Views

I've animated Riemann zeta function and got a spiral. Why?

Published on 26 Mar 2026 - 13:01

score 441 · Answer 8 · 2016-09-04 18:32:51

441

Views

sum of reciprocals of composite squarefree numbers

Published on 04 Sep 2016 - 18:32

score 726 · Answer 9 · 2026-03-25 17:44:37

726

Views

Where to find the paper of G.H. Hardy called "Sur les zéros de la fonction Zeta de Riemann" please?

Published on 25 Mar 2026 - 17:44

score 1.4k · Answer 10 · 2026-03-29 07:28:35

1.4k

Views

What are the modular forms which "naturally" corresponds to Riemann Zeta function or Dirichlet L function ?

Published on 29 Mar 2026 - 7:28

score 314 · Answer 11 · 2016-09-09 06:11:17

314

Views

The non-trivial zeroes of the Riemann Zeta Function

Published on 09 Sep 2016 - 6:11

score 123 · Answer 12 · 2016-09-10 05:34:53

123

Views

Are Li's numbers conditionally or absolutely convergent?

Published on 10 Sep 2016 - 5:34

score 157 · Answer 13 · 2026-03-27 15:36:18

157

Views

Irrationality of the Riemann zeta-function on odd arguments

Published on 27 Mar 2026 - 15:36

score 408 · Answer 14 · 2026-03-26 06:01:39

408

Views

Zeta function of algebraic variety over $\mathbb{F}_q$, formula for product of Witt vectors.

Published on 26 Mar 2026 - 6:01

score 824 · Answer 15 · 2026-03-25 22:11:06

824

Views

A Neat Identity Involving Zeta Zeroes

Published on 25 Mar 2026 - 22:11

List Question

Is $\sum_{n=1}^\infty \ln \left(1-\frac{1}{p_n^s} \right)=-\ln \zeta(s)$ the only known series with primes and nontrivial closed form?

Interesting connection between polylogarithms and polygamma functions.

Does Montgomery's pair correlation conjecture also hold true for Dedekind Zeta function ?

Relation between the derivative of hurwitz zeta and trigamma

What are some good introductory/elementary books on the Riemann zeta function?

Complex t in the Argument of the Zeta Function

I've animated Riemann zeta function and got a spiral. Why?

sum of reciprocals of composite squarefree numbers

Where to find the paper of G.H. Hardy called "Sur les zéros de la fonction Zeta de Riemann" please?

What are the modular forms which "naturally" corresponds to Riemann Zeta function or Dirichlet L function ?

The non-trivial zeroes of the Riemann Zeta Function

Are Li's numbers conditionally or absolutely convergent?

Irrationality of the Riemann zeta-function on odd arguments

Zeta function of algebraic variety over $\mathbb{F}_q$, formula for product of Witt vectors.

A Neat Identity Involving Zeta Zeroes

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