List questions from analytic-number-theory

Published on 11 May 2026 - 5:00

165

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Erdos-Kac implies the prime number theorem?

Published on 12 Apr 2026 - 20:56

262

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For what $k\in \mathbb{C}$ do we have $\lim_{x\to\infty}\frac{1}{x^{k+1}}\sum_{n=1}^x \sigma_k(n)=\frac{\zeta(k+1)}{k+1}$?

Published on 11 May 2026 - 1:54

132

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Discussion on problem 4.17.b in Apostol's analytic number theory

Published on 13 Apr 2026 - 10:13

172

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Proving an identity for $\sum_{m,n\in\mathbb{Z}_{>0}}\frac{\gcd(m,n)^r}{m^sn^t}$.

Published on 10 May 2026 - 19:41

394

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Interchanging summation involving divisors in index

Published on 10 May 2026 - 21:26

119

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Tail estimates for the sum $\sum_{n\geq 1} (1/ \varphi(n)^2)$

Published on 16 Apr 2026 - 12:05

346

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Growth of Digamma function

Published on 10 May 2026 - 14:29

59

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What is the behaviour of $Q^{-3}\sum_{Q<q\le 2Q} \varphi(q^2)$ as $Q\to\infty$?

Published on 13 Apr 2026 - 22:35

103

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How to prove that $\vartheta(x)=x+O(\frac x{\log(x)})$

Published on 14 Apr 2026 - 16:03

418

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Convexity Bound of Rankin-Selberg L-Function

Published on 10 May 2026 - 11:41

259

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What are the Fourier Transform of this function?

Published on 14 May 2026 - 19:37

130

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Show that the natural density is $1/2$.

Published on 14 Apr 2026 - 22:30

161

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Question in Iwaniec-Kowaleski's book : bound for a twisted series

Published on 13 Apr 2026 - 17:34

121

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Riemann zeta zeros Fourier like divergent square wave. Can you complete this analogy?

Published on 15 Apr 2026 - 13:10

List Question

On $\phi(n) \sigma(n)$ being a square.

Erdos-Kac implies the prime number theorem?

For what $k\in \mathbb{C}$ do we have $\lim_{x\to\infty}\frac{1}{x^{k+1}}\sum_{n=1}^x \sigma_k(n)=\frac{\zeta(k+1)}{k+1}$?

Discussion on problem 4.17.b in Apostol's analytic number theory

Proving an identity for $\sum_{m,n\in\mathbb{Z}_{>0}}\frac{\gcd(m,n)^r}{m^sn^t}$.

Interchanging summation involving divisors in index

Tail estimates for the sum $\sum_{n\geq 1} (1/ \varphi(n)^2)$

Growth of Digamma function

What is the behaviour of $Q^{-3}\sum_{Q<q\le 2Q} \varphi(q^2)$ as $Q\to\infty$?

How to prove that $\vartheta(x)=x+O(\frac x{\log(x)})$

Convexity Bound of Rankin-Selberg L-Function

What are the Fourier Transform of this function?

Show that the natural density is $1/2$.

Question in Iwaniec-Kowaleski's book : bound for a twisted series

Riemann zeta zeros Fourier like divergent square wave. Can you complete this analogy?

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