Question

Value of Riemann zeta function at $-1$

score 207 · Answer 1 · 2014-01-05 14:39:57

207

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Value of Riemann zeta function at $-1$

Published on 05 Jan 2014 - 14:39

score 180 · Answer 2 · 2026-03-27 21:20:29

180

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Can you prove that the $13$ first zeros of $(r\zeta(r+\Im i))^2$ have real part $r=\frac{1}{2}$, assuming LeClaire's approximation?

Published on 27 Mar 2026 - 21:20

score 354 · Answer 3 · 2014-01-05 19:13:12

354

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Compute $\zeta(2) = \frac{\pi^2}6$

Published on 05 Jan 2014 - 19:13

score 7.3k · Answer 4 · 2014-01-08 01:31:31

7.3k

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Does $\sum _{n=1}^{\infty } \frac{\sin(\text{ln}(n))}{n}$ converge?

Published on 08 Jan 2014 - 1:31

score 2.7k · Answer 5 · 2014-01-09 16:55:11

2.7k

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Does $\zeta(-1)=-1/12$ or $\zeta(-1) \to -1/12$?

Published on 09 Jan 2014 - 16:55

score 2.8k · Answer 6 · 2026-03-26 14:21:13

2.8k

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Have all the zeros of the Riemann Zeta function real part smaller than 1?

Published on 26 Mar 2026 - 14:21

score 308 · Answer 7 · 2014-01-13 11:07:54

308

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Closed form for $\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1)$

Published on 13 Jan 2014 - 11:07

score 596 · Answer 8 · 2014-01-13 13:00:32

596

Views

Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} - \frac{3}{32\pi^2}.$

Published on 13 Jan 2014 - 13:00

score 341 · Answer 9 · 2014-01-15 23:22:02

341

Views

Series involving the Riemann zeta function

Published on 15 Jan 2014 - 23:22

score 349 · Answer 10 · 2014-01-17 09:10:40

349

Views

A connection between a sequence from the Collatz conjecture and a sequence of densities from $\zeta(k)-1$?

Published on 17 Jan 2014 - 9:10

score 454 · Answer 11 · 2014-01-19 06:50:11

454

Views

Calculating $\zeta(0)$ by the residue of $\zeta(1)$

Published on 19 Jan 2014 - 6:50

score 95 · Answer 12 · 2014-01-19 17:58:52

95

Views

Are the zeros of the sum/difference of two reflexive, entire functions all on the line $\Re(s)=\frac12$?

Published on 19 Jan 2014 - 17:58

score 1.5k · Answer 13 · 2026-04-03 00:19:08

1.5k

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$1 + 1 + 1 +\cdots = -\frac{1}{2}$

Published on 03 Apr 2026 - 0:19

score 205 · Answer 14 · 2014-01-23 16:17:16

205

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Ways to calculate $\int_0^1 \frac{-\log x}{1+x}\ \mathrm dx$

Published on 23 Jan 2014 - 16:17

score 174 · Answer 15 · 2026-03-30 05:00:29

174

Views

Zeta function universality: How to compute the shift parameter for simple functions?

Published on 30 Mar 2026 - 5:00

List Question

Value of Riemann zeta function at $-1$

Can you prove that the $13$ first zeros of $(r\zeta(r+\Im i))^2$ have real part $r=\frac{1}{2}$, assuming LeClaire's approximation?

Compute $\zeta(2) = \frac{\pi^2}6$

Does $\sum _{n=1}^{\infty } \frac{\sin(\text{ln}(n))}{n}$ converge?

Does $\zeta(-1)=-1/12$ or $\zeta(-1) \to -1/12$?

Have all the zeros of the Riemann Zeta function real part smaller than 1?

Closed form for $\sum_{k=1}^{\infty} \zeta(2k)-\zeta(2k+1)$

Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} - \frac{3}{32\pi^2}.$

Series involving the Riemann zeta function

A connection between a sequence from the Collatz conjecture and a sequence of densities from $\zeta(k)-1$?

Calculating $\zeta(0)$ by the residue of $\zeta(1)$

Are the zeros of the sum/difference of two reflexive, entire functions all on the line $\Re(s)=\frac12$?

$1 + 1 + 1 +\cdots = -\frac{1}{2}$

Ways to calculate $\int_0^1 \frac{-\log x}{1+x}\ \mathrm dx$

Zeta function universality: How to compute the shift parameter for simple functions?

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