List questions from analytic-number-theory

Published on 13 Apr 2026 - 14:17

500

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Are there arbitrarily long prime gaps in which each number has at least three distinct prime factors?

Published on 14 Apr 2026 - 2:21

161

Views

Show that $\dfrac{\phi (n)}{n}=\sum\limits_{d|n} \dfrac{\mu (d)}{d}$

Published on 16 Apr 2026 - 1:49

217

Views

Dirichlet convolution of Möbius function with power of logarithm

Published on 11 Apr 2026 - 6:12

798

Views

Laurent expansion of $\zeta(s)$

Published on 14 Apr 2026 - 0:43

155

Views

A Gap in the Proof of the Duffin-Schaeffer's theorem

Published on 13 Apr 2026 - 14:24

52

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$\sum\limits _{d^{2}|n} \mu (d)=1$ if $n$ is square-free and $0$ otherwise.

Published on 15 Apr 2026 - 16:19

134

Views

Doubt regarding the proof of Prime Number Theorem

Published on 12 Apr 2026 - 21:37

415

Views

Inverse Laplace transform of the Riemann zeta function

Published on 14 Apr 2026 - 12:10

66

Views

What is this A constant and where does it come from?

Published on 12 Apr 2026 - 4:45

312

Views

Convergence rule for infinite product $\prod (1+a_n)$ with $a_n$ complex.

Published on 14 Apr 2026 - 16:22

54

Views

Boundness of Riemann zeta by log function

Published on 14 Apr 2026 - 12:10

1.4k

Views

Is Analytic Number Theory an active area of research

Published on 13 Apr 2026 - 12:04

417

Views

Closed form of $\sum_{n=1}^{\infty} \frac{1}{n(e^{2\pi n}+1)}$

Published on 13 Apr 2026 - 12:18

88

Views

Can $\pi(x)$ be obtained from this identity: $\ln(\zeta(s))=\int_2^\infty\frac{s\pi(x)}{x(x^{s}-1)}dx$ via some type of inversion?

Published on 16 Apr 2026 - 17:03

List Question

Simplifying $\frac{\zeta'(s)}{\zeta(s)}$

Are there arbitrarily long prime gaps in which each number has at least three distinct prime factors?

Show that $\dfrac{\phi (n)}{n}=\sum\limits_{d|n} \dfrac{\mu (d)}{d}$

Dirichlet convolution of Möbius function with power of logarithm

Laurent expansion of $\zeta(s)$

A Gap in the Proof of the Duffin-Schaeffer's theorem

$\sum\limits _{d^{2}|n} \mu (d)=1$ if $n$ is square-free and $0$ otherwise.

Doubt regarding the proof of Prime Number Theorem

Inverse Laplace transform of the Riemann zeta function

What is this A constant and where does it come from?

Convergence rule for infinite product $\prod (1+a_n)$ with $a_n$ complex.

Boundness of Riemann zeta by log function

Is Analytic Number Theory an active area of research

Closed form of $\sum_{n=1}^{\infty} \frac{1}{n(e^{2\pi n}+1)}$

Can $\pi(x)$ be obtained from this identity: $\ln(\zeta(s))=\int_2^\infty\frac{s\pi(x)}{x(x^{s}-1)}dx$ via some type of inversion?

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