Question

Write the sum $\sum\limits_{a \in \mathbb{N}}\sum\limits_{b \in \mathbb{N}} \frac{(a,b)}{a^sb^t}$ in terms of the Riemann zeta function

score 264 · Answer 1 · 2026-04-15 20:46:58

264

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Write the sum $\sum\limits_{a \in \mathbb{N}}\sum\limits_{b \in \mathbb{N}} \frac{(a,b)}{a^sb^t}$ in terms of the Riemann zeta function

Published on 15 Apr 2026 - 20:46

score 64 · Answer 2 · 2026-04-10 13:28:53

64

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analytic continuation of the spectral zeta function

Published on 10 Apr 2026 - 13:28

score 226 · Answer 3 · 2026-04-10 19:49:00

226

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What is $x^\bot$? Is $\zeta(\bot)=\bot$ for Riemann's zeta function $\zeta$ and wheel theory's $\bot$?

Published on 10 Apr 2026 - 19:49

score 113 · Answer 4 · 2026-04-10 18:25:55

113

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Is this true of the Reimann zeta function?

Published on 10 Apr 2026 - 18:25

score 165 · Answer 5 · 2026-04-13 23:01:56

165

Views

On the zeros of the Riemann Zeta function

Published on 13 Apr 2026 - 23:01

score 124 · Answer 6 · 2026-04-13 13:35:12

124

Views

What is the sum $\sum_{(m, n)\in\mathbb{Z}\\(m,n)\neq(0,0)}\frac{1}{(m+in)^\alpha}$ equal to?

Published on 13 Apr 2026 - 13:35

score 95 · Answer 7 · 2026-04-16 13:04:39

95

Views

Swapping the series and product in the zeta function euler product equality

Published on 16 Apr 2026 - 13:04

score 58 · Answer 8 · 2026-04-16 05:52:43

58

Views

What is the qualitative relationship between an analytic function and its analytic continuation on the complement of the originally defined domain?

Published on 16 Apr 2026 - 5:52

score 169 · Answer 9 · 2026-03-28 05:23:10

169

Views

Given $a \ge 0$ and $b \gt 1$, and large $n$, how to approximate $x$; $1 =\frac{1}{n^ax}+\frac{1}{n}\sum_{k=1}^\infty\frac{1}{1+k^bx}$

Published on 28 Mar 2026 - 5:23

score 159 · Answer 10 · 2026-04-09 00:18:47

159

Views

Explicit Taylor Expansions of Zeta Function

Published on 09 Apr 2026 - 0:18

score 321 · Answer 11 · 2026-04-14 00:36:38

321

Views

Is there an absolute mimumum distance between zeros of the Riemann zeta function?

Published on 14 Apr 2026 - 0:36

score 48 · Answer 12 · 2026-04-12 23:24:05

48

Views

Does the path $t \mapsto \zeta(\frac 12 + it)$ eventually stay clockwise?

Published on 12 Apr 2026 - 23:24

score 60 · Answer 13 · 2026-04-13 07:13:18

60

Views

Is $p^s$ transcendental if $\zeta(s)=0$?

Published on 13 Apr 2026 - 7:13

score 156 · Answer 14 · 2026-04-15 01:34:24

156

Views

Computation on converging alternating zeta-like series by analytic continuation

Published on 15 Apr 2026 - 1:34

score 105 · Answer 15 · 2026-04-15 16:03:39

105

Views

Prove $|n^s| = n^{Re(s)}$

Published on 15 Apr 2026 - 16:03

List Question

Write the sum $\sum\limits_{a \in \mathbb{N}}\sum\limits_{b \in \mathbb{N}} \frac{(a,b)}{a^sb^t}$ in terms of the Riemann zeta function

analytic continuation of the spectral zeta function

What is $x^\bot$? Is $\zeta(\bot)=\bot$ for Riemann's zeta function $\zeta$ and wheel theory's $\bot$?

Is this true of the Reimann zeta function?

On the zeros of the Riemann Zeta function

What is the sum $\sum_{(m, n)\in\mathbb{Z}\\(m,n)\neq(0,0)}\frac{1}{(m+in)^\alpha}$ equal to?

Swapping the series and product in the zeta function euler product equality

What is the qualitative relationship between an analytic function and its analytic continuation on the complement of the originally defined domain?

Given $a \ge 0$ and $b \gt 1$, and large $n$, how to approximate $x$; $1 =\frac{1}{n^ax}+\frac{1}{n}\sum_{k=1}^\infty\frac{1}{1+k^bx}$

Explicit Taylor Expansions of Zeta Function

Is there an absolute mimumum distance between zeros of the Riemann zeta function?

Does the path $t \mapsto \zeta(\frac 12 + it)$ eventually stay clockwise?

Is $p^s$ transcendental if $\zeta(s)=0$?

Computation on converging alternating zeta-like series by analytic continuation

Prove $|n^s| = n^{Re(s)}$

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