List questions from analytic-number-theory

Published on 25 Mar 2026 - 7:43

116

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Probability that a random number avoids a set of prime divisors

Published on 25 Mar 2026 - 13:28

201

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A bound for a sum over square-free numbers: $\sum_{n \leq X} \frac{\mu(n)^2 \tau_k(n)}{\phi(n)} \ll (\log X)^k$

Published on 26 Mar 2026 - 4:33

85

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Are there infinitely many numbers $n$ with $\phi(n) = \pi(n) + \omega(n)$?

Published on 15 May 2018 - 9:43

42

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Show $O\left(\sqrt x\right) + \int_{\sqrt{x}}^{x}\frac{\pi(t)}{t}dt <<\frac{x}{\ln x}$

Published on 17 May 2018 - 1:16

645

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The asymptotics of the products over primes $\prod\limits_{2<p\le n}\left(1 - \frac1{p-1}\right)$

Published on 25 Mar 2026 - 1:18

238

Views

Quadratic Gauss sum for prime powers

Published on 22 May 2018 - 8:38

136

Views

Bounds for Dedekind Zeta functions

Published on 23 May 2018 - 15:41

91

Views

A-x, B+x, x is all perfect square (Diophantine equation)

Published on 24 May 2018 - 14:45

664

Views

Good Books on Complex Multiplication (on Elliptic Curves)

Published on 26 Mar 2026 - 15:27

111

Views

Inequality with sum involving minimums

Published on 25 Mar 2026 - 17:02

526

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How to prove that the values of Eisenstein Series $E_2$ are algebraic integers?

Published on 26 Mar 2026 - 15:29

414

Views

help with a simple example of the Hardy-Littlewood circle method.

Published on 26 May 2018 - 19:12

67

Views

What is the uniquely determined multiplicative function which agrees with $f$ at the prime powers?

Published on 28 May 2018 - 7:39

47

Views

Is it necessary that $a\ge b$ to $h(n)=\sum\limits_{d^a|n}f(\frac n{d^a})g(\frac n{d^b})$ be multiplicative

Published on 28 May 2018 - 10:53

List Question

On a product involving Ramanujan primes

Probability that a random number avoids a set of prime divisors

A bound for a sum over square-free numbers: $\sum_{n \leq X} \frac{\mu(n)^2 \tau_k(n)}{\phi(n)} \ll (\log X)^k$

Are there infinitely many numbers $n$ with $\phi(n) = \pi(n) + \omega(n)$?

Show $O\left(\sqrt x\right) + \int_{\sqrt{x}}^{x}\frac{\pi(t)}{t}dt <<\frac{x}{\ln x}$

The asymptotics of the products over primes $\prod\limits_{2<p\le n}\left(1 - \frac1{p-1}\right)$

Quadratic Gauss sum for prime powers

Bounds for Dedekind Zeta functions

A-x, B+x, x is all perfect square (Diophantine equation)

Good Books on Complex Multiplication (on Elliptic Curves)

Inequality with sum involving minimums

How to prove that the values of Eisenstein Series $E_2$ are algebraic integers?

help with a simple example of the Hardy-Littlewood circle method.

What is the uniquely determined multiplicative function which agrees with $f$ at the prime powers?

Is it necessary that $a\ge b$ to $h(n)=\sum\limits_{d^a|n}f(\frac n{d^a})g(\frac n{d^b})$ be multiplicative

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