List questions from analytic-number-theory

Published on 15 Apr 2026 - 18:28

255

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The inverse of a Dirichlet product is the Dirichlet product of the inverses of each function

Published on 14 Apr 2026 - 14:29

102

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Prove that $\sum\limits_{n=1}^{N} \frac{1}{n} \le \text{exp}\left(2\sum\limits_{n=1}^{N} p_k^{-1}\right)$

Published on 15 Apr 2026 - 5:31

251

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Chebyshev function: variational formulation

Published on 10 May 2026 - 14:02

299

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Convergence of $\sum\limits_p \frac{\chi(p)}{p}$ and the prime number theorem

Published on 13 Apr 2026 - 23:39

59

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About absolute convergence of complex series

Published on 10 Apr 2026 - 20:04

432

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Density of integers $n$ with all prime factors of order $O(\log n)$?

Published on 17 Apr 2026 - 9:00

304

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Number of integers coprime to a given integer $q$ in some range $[x, x+y]$

Published on 09 Apr 2026 - 5:50

37

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Solutions for $n$? Use Stirling approximations if needed

Published on 10 Apr 2026 - 21:50

55

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Show $\frac{\sum_{n=1}^{\infty}\frac{1}{\phi(n)^s}}{\zeta(s)}=\prod_{p}(1-1/p^s+1/(p-1)^s)$.

Published on 31 Mar 2026 - 13:17

231

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The limit on the ratio of the Dirichlet eta functions

Published on 16 Apr 2026 - 16:00

42

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A not very obvious question about $\{h+tk\}$ sequence.

Published on 09 Apr 2026 - 5:49

404

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An Engineer sets out to Prove Fermat's Last Theorem ...

Published on 10 May 2026 - 15:51

198

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If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.

Published on 14 May 2026 - 20:27

78

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Estimating $\sum\limits_{n\leq x} d_3(n)$.

Published on 15 Apr 2026 - 9:54

List Question

Lower bound for number of primes up to $x$.

The inverse of a Dirichlet product is the Dirichlet product of the inverses of each function

Prove that $\sum\limits_{n=1}^{N} \frac{1}{n} \le \text{exp}\left(2\sum\limits_{n=1}^{N} p_k^{-1}\right)$

Chebyshev function: variational formulation

Convergence of $\sum\limits_p \frac{\chi(p)}{p}$ and the prime number theorem

About absolute convergence of complex series

Density of integers $n$ with all prime factors of order $O(\log n)$?

Number of integers coprime to a given integer $q$ in some range $[x, x+y]$

Solutions for $n$? Use Stirling approximations if needed

Show $\frac{\sum_{n=1}^{\infty}\frac{1}{\phi(n)^s}}{\zeta(s)}=\prod_{p}(1-1/p^s+1/(p-1)^s)$.

The limit on the ratio of the Dirichlet eta functions

A not very obvious question about $\{h+tk\}$ sequence.

An Engineer sets out to Prove Fermat's Last Theorem ...

If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.

Estimating $\sum\limits_{n\leq x} d_3(n)$.

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