Question

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

score 84 · Answer 1 · 2021-02-22 22:26:10

84

Views

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Published on 22 Feb 2021 - 22:26

score 97 · Answer 2 · 2021-03-06 03:58:09

97

Views

Why is Euler product destroyed?

Published on 06 Mar 2021 - 3:58

score 118 · Answer 3 · 2021-03-15 23:56:42

118

Views

Why is Euler's statement $\exp{(A + \frac{1}{2}B + \frac{1}{3}C+ \ldots)} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots$ true?

Published on 15 Mar 2021 - 23:56

score 172 · Answer 4 · 2021-03-25 14:59:42

172

Views

validity of proof $\pi$ is irrational from Euler's product formula

Published on 25 Mar 2021 - 14:59

score 59 · Answer 5 · 2021-04-06 00:18:52

59

Views

Using Viete's Product show that $\frac{3}{\pi}= \frac{\sqrt{2+\sqrt{3}}}{2} * \frac{\sqrt{2+\sqrt{2+\sqrt{3}}}}{2} * ...$

Published on 06 Apr 2021 - 0:18

score 94 · Answer 6 · 2021-04-22 12:19:13

94

Views

Does this sum of two Euler products converge for $s=1$?

Published on 22 Apr 2021 - 12:19

score 133 · Answer 7 · 2021-04-24 17:45:31

133

Views

Validity of taking log of divergent sums in proof $\sum 1/p \rightarrow \infty$

Published on 24 Apr 2021 - 17:45

score 190 · Answer 8 · 2021-06-13 10:04:00

190

Views

A prime numbers property: $4/\pi=e^{1/2}\Big(1+e^{1/3}\big(1+e^{1/5}(\dots)\big)\Big)/p_n, \ \ n\to\infty$

Published on 13 Jun 2021 - 10:04

score 228 · Answer 9 · 2021-07-31 22:04:22

228

Views

Validity of proof $\zeta(s) \neq 0$ for $\sigma\gt1$, where $\sigma$ is the real part of $s$

Published on 31 Jul 2021 - 22:04

score 85 · Answer 10 · 2021-08-13 21:59:40

85

Views

Trying to prove that $\varphi(s)$ is related to prime numbers

Published on 13 Aug 2021 - 21:59

score 37 · Answer 11 · 2021-08-30 20:55:43

37

Views

A way of splitting Euler products

Published on 30 Aug 2021 - 20:55

score 142 · Answer 12 · 2021-09-25 14:00:00

142

Views

Are there extensions of Euler's infinite product for sine function?

Published on 25 Sep 2021 - 14:00

score 60 · Answer 13 · 2022-01-06 21:28:58

60

Views

A variant of the Euler product formula?

Published on 06 Jan 2022 - 21:28

score 123 · Answer 14 · 2022-03-19 06:24:43

123

Views

How to prove that $\sqrt{3}\pi/6=\prod_{p \equiv 1 \pmod{6}} \frac{p}{p-1}\prod_{p \equiv 5 \pmod{6}} \frac{p}{p+1}$ with $p \in \mathbb{P}$?

Published on 19 Mar 2022 - 6:24

score 78 · Answer 15 · 2022-03-26 19:32:38

78

Views

Does the Euler product for the Rankin-Selberg convolution of two eigenforms require the Ramanujan conjecture?

Published on 26 Mar 2022 - 19:32

List Question

Where does $\frac{3}{2}$ in $1<s\cdot\zeta(s+1) < \frac{3}{2}$ come from?

Why is Euler product destroyed?

Why is Euler's statement $\exp{(A + \frac{1}{2}B + \frac{1}{3}C+ \ldots)} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots$ true?

validity of proof $\pi$ is irrational from Euler's product formula

Using Viete's Product show that $\frac{3}{\pi}= \frac{\sqrt{2+\sqrt{3}}}{2} * \frac{\sqrt{2+\sqrt{2+\sqrt{3}}}}{2} * ...$

Does this sum of two Euler products converge for $s=1$?

Validity of taking log of divergent sums in proof $\sum 1/p \rightarrow \infty$

A prime numbers property: $4/\pi=e^{1/2}\Big(1+e^{1/3}\big(1+e^{1/5}(\dots)\big)\Big)/p_n, \ \ n\to\infty$

Validity of proof $\zeta(s) \neq 0$ for $\sigma\gt1$, where $\sigma$ is the real part of $s$

Trying to prove that $\varphi(s)$ is related to prime numbers

A way of splitting Euler products

Are there extensions of Euler's infinite product for sine function?

A variant of the Euler product formula?

How to prove that $\sqrt{3}\pi/6=\prod_{p \equiv 1 \pmod{6}} \frac{p}{p-1}\prod_{p \equiv 5 \pmod{6}} \frac{p}{p+1}$ with $p \in \mathbb{P}$?

Does the Euler product for the Rankin-Selberg convolution of two eigenforms require the Ramanujan conjecture?

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