List questions from analytic-number-theory

Published on 11 May 2026 - 23:09

138

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About the corvergence of series involving Stirling numbers of first kind and number theoretic functions

Published on 06 May 2026 - 6:31

173

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Reference for von Koch's 1901 theorem (RH characterization)

Published on 29 Apr 2026 - 12:42

1.3k

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Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Published on 29 Apr 2026 - 12:51

54

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Show that this sum is the length of an interval I

Published on 29 Apr 2026 - 0:29

45

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On existence of certain integers?

Published on 29 Apr 2026 - 0:27

101

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A symbolic combination of an inequality concerning convergent series and Brun's theorem: improving the upper bound

Published on 12 May 2026 - 7:25

218

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Bound on Divisor Counting Function

Published on 29 Apr 2026 - 12:50

67

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A question regarding $\nu_p(2^{p-1} - 1)$ from AoPS

Published on 29 Apr 2026 - 0:29

1.1k

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A bound on number of divisors of $n$

Published on 10 May 2026 - 12:34

694

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The asymptotic behaviour of a sequence involving the sine and cosine functions: explain an strategy to get it

Published on 29 Apr 2026 - 9:56

136

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Integral of Gamma Functions

Published on 10 May 2026 - 16:00

92

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Estimating $\sum\limits_{2\le n,m\le X}\frac{\Lambda(n)\Lambda(m)}{(nm)^\sigma\log(n)\log(m)}$

Published on 10 May 2026 - 16:01

179

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Why $\sum\frac{\mu(h)\mu(k)}{hk}\gcd(h,k)=\prod\limits_{p\le x}\left(1-\frac1p\right)$, where the sum enumerates the pairs $(h,k)$ of primes below $x$

Published on 07 May 2026 - 3:53

349

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What is the closed-form of $\sum_{n=1}^\infty\lambda(n)\log\cosh\frac{1}{n}$, where $\lambda(n)$ is the Liouville function?

Published on 10 May 2026 - 16:12

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Real solution of equations of 2018

About the corvergence of series involving Stirling numbers of first kind and number theoretic functions

Reference for von Koch's 1901 theorem (RH characterization)

Elementary proof that the limit of $\sum_{i=1}^{\infty} \frac{1}{\operatorname{lcm}(1,2,...,i)}$ is irrational

Show that this sum is the length of an interval I

On existence of certain integers?

A symbolic combination of an inequality concerning convergent series and Brun's theorem: improving the upper bound

Bound on Divisor Counting Function

A question regarding $\nu_p(2^{p-1} - 1)$ from AoPS

A bound on number of divisors of $n$

The asymptotic behaviour of a sequence involving the sine and cosine functions: explain an strategy to get it

Integral of Gamma Functions

Estimating $\sum\limits_{2\le n,m\le X}\frac{\Lambda(n)\Lambda(m)}{(nm)^\sigma\log(n)\log(m)}$

Why $\sum\frac{\mu(h)\mu(k)}{hk}\gcd(h,k)=\prod\limits_{p\le x}\left(1-\frac1p\right)$, where the sum enumerates the pairs $(h,k)$ of primes below $x$

What is the closed-form of $\sum_{n=1}^\infty\lambda(n)\log\cosh\frac{1}{n}$, where $\lambda(n)$ is the Liouville function?

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