List questions from analytic-number-theory

Published on 13 Feb 2019 - 22:01

252

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

Published on 13 Feb 2019 - 22:41

99

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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 14 Feb 2019 - 10:35

248

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Chebyshev function: variational formulation

Published on 30 Mar 2026 - 9:28

296

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

Published on 15 Feb 2019 - 1:22

56

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About absolute convergence of complex series

Published on 15 Feb 2019 - 12:32

428

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

Published on 26 Mar 2026 - 6:22

303

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

Published on 23 Feb 2026 - 2:58

35

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Solutions for $n$? Use Stirling approximations if needed

Published on 26 Mar 2026 - 12:13

54

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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 26 Mar 2026 - 2:57

228

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The limit on the ratio of the Dirichlet eta functions

Published on 20 Feb 2019 - 8:58

41

Views

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

Published on 23 Feb 2026 - 2:54

403

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

Published on 25 Mar 2026 - 13:42

194

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

Published on 19 Mar 2026 - 22:56

75

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

Published on 22 Feb 2019 - 11:38

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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