Question

Derive Xi Function's Infinite Product

score 230 · Answer 1 · 2026-04-11 08:16:46

230

Views

Derive Xi Function's Infinite Product

Published on 11 Apr 2026 - 8:16

score 129 · Answer 2 · 2026-03-27 12:16:19

129

Views

Gram series in Riemann explicit formula for π(x)

Published on 27 Mar 2026 - 12:16

score 105 · Answer 3 · 2026-03-25 11:12:12

105

Views

How does one arrive at the basic limit formulation for the Stieltjes constants?

Published on 25 Mar 2026 - 11:12

score 24 · Answer 4 · 2026-04-11 12:20:28

24

Views

Convergence of alternting series of complex numbers in Riemann Zeta

Published on 11 Apr 2026 - 12:20

score 68 · Answer 5 · 2026-04-12 20:59:35

68

Views

Proof of convergence, or lack thereof, of the real-line integral formula for the Riemann zeta function for Re(s)>1

Published on 12 Apr 2026 - 20:59

score 240 · Answer 6 · 2026-03-25 16:45:37

240

Views

Is there an elementary proof for the weak prime number theorem?

Published on 25 Mar 2026 - 16:45

score 152 · Answer 7 · 2026-03-27 17:53:08

152

Views

Proving $\prod_{n=0}^{\infty}\left(1+\frac{x}{a^n}\right)=\sum_{n=0}^{\infty}\frac{(ax)^n}{\prod_{k=1}^{n}(a^k-1)}$

Published on 27 Mar 2026 - 17:53

score 159 · Answer 8 · 2026-03-26 04:16:03

159

Views

Conditional convergence of the Hadamard product

Published on 26 Mar 2026 - 4:16

score 214 · Answer 9 · 2022-01-02 21:54:17

214

Views

Proving Euler's product form of the Riemann zeta function

Published on 02 Jan 2022 - 21:54

score 51 · Answer 10 · 2026-03-31 15:45:01

51

Views

counting primes on different scales than the normal one

Published on 31 Mar 2026 - 15:45

score 102 · Answer 11 · 2026-04-12 16:23:02

102

Views

$\zeta(1 + 2/x)$ has a strange, nearly linear behaviour

Published on 12 Apr 2026 - 16:23

score 149 · Answer 12 · 2022-01-08 13:24:11

149

Views

On line integral $\displaystyle\int_{a + i\infty}^{a - i\infty} \frac{\zeta^2(1-s)\zeta^2(s-4m-1)}{2 \cos\left(\frac{\pi s}{2}\right)} \,\mathrm{d}s$

Published on 08 Jan 2022 - 13:24

score 283 · Answer 13 · 2022-01-08 21:27:42

283

Views

Multiplicative order of 2 mod p

Published on 08 Jan 2022 - 21:27

score 150 · Answer 14 · 2022-01-13 23:49:03

is it true that $\zeta(\frac{1}{2} + bi) = 0 \implies \zeta(a + bi) \neq 0$ for $0 < a < 1$, $a\neq \frac{1}{2}$?

score 273 · Answer 15 · 2026-03-27 02:59:44

273

Views

What computer methods are used to quickly calculate the $\zeta$-function (if any)?

Published on 27 Mar 2026 - 2:59

List Question

Derive Xi Function's Infinite Product

Gram series in Riemann explicit formula for π(x)

How does one arrive at the basic limit formulation for the Stieltjes constants?

Convergence of alternting series of complex numbers in Riemann Zeta

Proof of convergence, or lack thereof, of the real-line integral formula for the Riemann zeta function for Re(s)>1

Is there an elementary proof for the weak prime number theorem?

Proving $\prod_{n=0}^{\infty}\left(1+\frac{x}{a^n}\right)=\sum_{n=0}^{\infty}\frac{(ax)^n}{\prod_{k=1}^{n}(a^k-1)}$

Conditional convergence of the Hadamard product

Proving Euler's product form of the Riemann zeta function

counting primes on different scales than the normal one

$\zeta(1 + 2/x)$ has a strange, nearly linear behaviour

On line integral $\displaystyle\int_{a + i\infty}^{a - i\infty} \frac{\zeta^2(1-s)\zeta^2(s-4m-1)}{2 \cos\left(\frac{\pi s}{2}\right)} \,\mathrm{d}s$

Multiplicative order of 2 mod p

is it true that $\zeta(\frac{1}{2} + bi) = 0 \implies \zeta(a + bi) \neq 0$ for $0 < a < 1$, $a\neq \frac{1}{2}$?

What computer methods are used to quickly calculate the $\zeta$-function (if any)?

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