Question

$\int_{-\infty}^{\infty} \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ where $\zeta$ is the Riemann zeta function

score 348 · Answer 1 · 2026-04-16 16:03:50

348

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$\int_{-\infty}^{\infty} \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ where $\zeta$ is the Riemann zeta function

Published on 16 Apr 2026 - 16:03

score 126 · Answer 2 · 2026-04-09 22:07:13

126

Views

The Zeta Function and the Prime Number Theorem

Published on 09 Apr 2026 - 22:07

score 341 · Answer 3 · 2026-04-13 12:02:03

341

Views

Jensen's Formula application $f(z)$ has no zeros on $|z|=r, r<1$

Published on 13 Apr 2026 - 12:02

score 285 · Answer 4 · 2026-04-14 15:10:49

285

Views

Euler product over a finite subset of composite numbers

Published on 14 Apr 2026 - 15:10

score 131 · Answer 5 · 2026-04-15 20:11:20

131

Views

A result of Chebychev and an $\epsilon$ away from Bertrand's postulate

Published on 15 Apr 2026 - 20:11

score 83 · Answer 6 · 2026-04-10 18:48:31

83

Views

How does this product over finite primes represents density of certain natural numbers?

Published on 10 Apr 2026 - 18:48

score 76 · Answer 7 · 2026-04-09 16:36:42

76

Views

Confusion with notation for Dirichlet characters

Published on 09 Apr 2026 - 16:36

score 137 · Answer 8 · 2026-04-14 07:30:43

137

Views

On a certain integral related to Euler-Masheroni constant

Published on 14 Apr 2026 - 7:30

score 28 · Answer 9 · 2026-04-15 08:15:16

28

Views

Asymptotics of a sum involving multiplicative partitions of an integer $n$ into $k$ possibly non-distinct parts $≥2$

Published on 15 Apr 2026 - 8:15

score 100 · Answer 10 · 2026-04-12 04:35:02

100

Views

Proof that the product of $L$-function over all Dirichlet characters is not less than 1 (from Fourier Analysis by Stein)

Published on 12 Apr 2026 - 4:35

score 65 · Answer 11 · 2026-04-13 21:18:40

65

Views

Sum of Legendre symbols over interval for primes of particular form.

Published on 13 Apr 2026 - 21:18

score 424 · Answer 12 · 2026-04-16 00:43:54

424

Views

Validity of simple intuition for $\sum 1/p \sim \log \log n$ work?

Published on 16 Apr 2026 - 0:43

score 77 · Answer 13 · 2026-04-16 09:55:35

77

Views

Find an asymptotic upper bound for $\prod_{p|n}(1+\frac{2}{p})$.

Published on 16 Apr 2026 - 9:55

score 46 · Answer 14 · 2026-04-16 07:46:54

46

Views

What is the coefficient of $q^n$ in the Lambert Series Expansion $a^2(q).a(q^5)$

Published on 16 Apr 2026 - 7:46

score 120 · Answer 15 · 2026-04-15 14:46:51

120

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 Apr 2026 - 14:46

List Question

$\int_{-\infty}^{\infty} \frac{\log|\zeta(\frac{1}{2}+it)|}{\frac{1}{4}+t^2}dt$ where $\zeta$ is the Riemann zeta function

The Zeta Function and the Prime Number Theorem

Jensen's Formula application $f(z)$ has no zeros on $|z|=r, r<1$

Euler product over a finite subset of composite numbers

A result of Chebychev and an $\epsilon$ away from Bertrand's postulate

How does this product over finite primes represents density of certain natural numbers?

Confusion with notation for Dirichlet characters

On a certain integral related to Euler-Masheroni constant

Asymptotics of a sum involving multiplicative partitions of an integer $n$ into $k$ possibly non-distinct parts $≥2$

Proof that the product of $L$-function over all Dirichlet characters is not less than 1 (from Fourier Analysis by Stein)

Sum of Legendre symbols over interval for primes of particular form.

Validity of simple intuition for $\sum 1/p \sim \log \log n$ work?

Find an asymptotic upper bound for $\prod_{p|n}(1+\frac{2}{p})$.

What is the coefficient of $q^n$ in the Lambert Series Expansion $a^2(q).a(q^5)$

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?

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