A. Shubin

activity

20202026

collaborators

5 papers

math.NT2026

Circle coverings driven by arithmetic sequences: a percolation approach to Diophantine approximation and fractal intersections

Manuel Hauke, Andrei Shubin, Eduard Stefanescu +1

We study problems on covering $[0, 1)$ by shrinking intervals centered at the points ${q_{n} x}$ , where $(q_{n})_{n \in N}$ is a given real-valued sequence and $x \in [0, 1)$ i…

math.NT2022

Möbius orthogonality of Thue-Morse sequence along Piatetski-Shapiro numbers

Andrei Shubin

We show that the Möbius function is orthogonal to the Thue-Morse sequence $t (n)$ taken along the Piatetski-Shapiro numbers $⌊ n^{c} ⌋$ for any $1 < c < 2$ . Previously thi…

math.NT2021

Variance estimates in Linnik's problem

Andrei Shubin

We evaluate the variance of the number of lattice points in a small randomly rotated spherical ball on a surface of 3-dimensional sphere centered at the origin. Previously, Bourgai…

math.NT2020

Fractional parts of non-integer powers of primes. II

Andrei Shubin

We continue to study the distribution of prime numbers $p$ , satisfying the condition ${p^{α}} \in I \subset [0; 1)$ , in arithmetic progressions. In the paper, we prove an analogu…

math.NT2020

Fractional parts of non-integer powers of primes

Andrei Shubin

Let $α > 0$ be any fixed non-integer, $I$ be any subinterval of $[0; 1)$ . In the paper, we prove an analogue of Bombieri-Vinogradov theorem for the set of primes $p$ satisfying the…