Mikhail R. Gabdullin

activity

20162025

collaborators

5 papers

math.NT2025

Moments of the shifted prime divisor function

Mikhail R. Gabdullin

Let $ω^*(n) = \{d|n: d=p-1, \mbox{$p$ is a prime}\}$. We show that, for each integer $k \geq 2$ , $n \leq x \sum ω^{*} (n)^{k} ≍ x (lo g x)^{2^{k} - k - 1},$ where the implied constant m…

math.NT2024

Primes with small primitive roots

Kevin Ford, Mikhail R. Gabdullin, Andrew Granville

Let $δ (p)$ tend to zero arbitrarily slowly as $p \to \infty$ . We exhibit an explicit set $S$ of primes $p$ , defined in terms of simple functions of the prime factors of $p-…

math.NT2023

Long strings of consecutive composite values of polynomials

Kevin Ford, Mikhail R. Gabdullin

We show that for any polynomial $f$ from the integers to the integers, with positive leading coefficient and irreducible over the rationals, if $x$ is large enough then there is a…

math.NT2020

Sets whose differences avoid squares modulo m

Kevin Ford, Mikhail R. Gabdullin

We prove that if $ε (m) \to 0$ arbitrarily slowly, then for almost all $m$ and any $A \subset Z_{m}$ such that $A - A$ does not contain non-zero quadratic residues we ha…

math.NT2016

Set avoiding squares in $Z_{m}$

Mikhail Gabdullin

We prove that for all squarefree $m$ and any set $A \subset Z_{m}$ such that $A - A$ does not contain non-zero squares the bound $∣ A ∣ \leq m^{1/2} (3 n)^{1.5 n}$ holds, where $n$ de…

Moments of the shifted prime divisor function

Primes with small primitive roots

Long strings of consecutive composite values of polynomials

Sets whose differences avoid squares modulo m

Set avoiding squares in Zm​

Set avoiding squares in $Z_{m}$