List questions from analytic-number-theory

Published on 09 Apr 2026 - 12:16

326

Views

Can the inverse of the Riemann zeta function in $s > 1$ be expressed as a series?

Published on 12 Apr 2026 - 6:07

79

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Proportion of non-quadratic residues when added by 1 are still non-quadratic residues

Published on 14 Apr 2026 - 4:35

108

Views

Is there a sequence of rational numbers $a_n$ such that $a_1 e^{-1} + a_2 e^{-2} + \cdots = 1$?

Published on 16 Apr 2026 - 9:14

145

Views

Apostol's unexplained claim $\frac{x^{1-s}}{1-s}$ is 0 in Euler sum expansion of $\sum_{n \leq x} \frac{1}{n^s} $

Published on 15 Apr 2026 - 20:16

57

Views

Error bound in the P.N.T. under some R.H.-like assumption

Published on 15 Apr 2026 - 5:52

365

Views

What is the most frequent largest prime factor of the numbers between two primes?

Published on 13 Apr 2026 - 15:13

111

Views

A question about the Theta functions

Published on 10 Apr 2026 - 1:50

153

Views

The integral of a (dyadic) sum

Published on 14 Apr 2026 - 15:15

57

Views

$\sum_{p,m\geq 3}(-1)^{m(p-1)/2}e^{-p^my}\log p = O(y^{-1/3})$

Published on 17 Apr 2026 - 10:36

65

Views

Zeros of a family of number theoretic polynomials

Published on 14 Apr 2026 - 8:31

153

Views

Find $\sum_{n=1}^{\infty} \frac{n^{\sigma -1} (n+\sigma )-(n+1)^{\sigma }}{\sigma(1-\sigma)}$ for $ 0<\sigma<1$

Published on 25 Mar 2026 - 6:12

305

Views

Riemann Zeta function's analytic continuation relationship with simple closed formulas

Published on 09 Apr 2026 - 16:38

52

Views

Green's functions for noncompact finite-volume quotient

Published on 13 Apr 2026 - 20:26

142

Views

Is $N=2^{2^n}+2^{2^{n-1}}+2^{2^{n-2}}+2^{2^{n-3}} + \ldots+ 2^{2^3}+2^{2^2}+n$ is always composite?

Published on 17 Apr 2026 - 5:06

List Question

Problem with the Möbius Inversion Formula

Can the inverse of the Riemann zeta function in $s > 1$ be expressed as a series?

Proportion of non-quadratic residues when added by 1 are still non-quadratic residues

Is there a sequence of rational numbers $a_n$ such that $a_1 e^{-1} + a_2 e^{-2} + \cdots = 1$?

Apostol's unexplained claim $\frac{x^{1-s}}{1-s}$ is 0 in Euler sum expansion of $\sum_{n \leq x} \frac{1}{n^s} $

Error bound in the P.N.T. under some R.H.-like assumption

What is the most frequent largest prime factor of the numbers between two primes?

A question about the Theta functions

The integral of a (dyadic) sum

$\sum_{p,m\geq 3}(-1)^{m(p-1)/2}e^{-p^my}\log p = O(y^{-1/3})$

Zeros of a family of number theoretic polynomials

Find $\sum_{n=1}^{\infty} \frac{n^{\sigma -1} (n+\sigma )-(n+1)^{\sigma }}{\sigma(1-\sigma)}$ for $ 0<\sigma<1$

Riemann Zeta function's analytic continuation relationship with simple closed formulas

Green's functions for noncompact finite-volume quotient

Is $N=2^{2^n}+2^{2^{n-1}}+2^{2^{n-2}}+2^{2^{n-3}} + \ldots+ 2^{2^3}+2^{2^2}+n$ is always composite?

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