List questions from analytic-number-theory

Published on 10 May 2026 - 16:33

121

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Probability that a random number avoids a set of prime divisors

Published on 13 May 2026 - 17:42

205

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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 14 May 2026 - 11:07

88

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

Published on 13 Apr 2026 - 17:15

44

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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 15 Apr 2026 - 10:00

648

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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 10 May 2026 - 15:25

241

Views

Quadratic Gauss sum for prime powers

Published on 11 Apr 2026 - 6:15

138

Views

Bounds for Dedekind Zeta functions

Published on 08 Apr 2026 - 13:59

94

Views

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

Published on 15 Apr 2026 - 21:58

667

Views

Good Books on Complex Multiplication (on Elliptic Curves)

Published on 13 May 2026 - 18:48

117

Views

Inequality with sum involving minimums

Published on 14 May 2026 - 1:07

529

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

Published on 13 May 2026 - 18:49

417

Views

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

Published on 13 Apr 2026 - 13:45

69

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

Published on 09 Apr 2026 - 22:22

50

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 15 Apr 2026 - 14:05

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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