Steklov Mathematical Institute

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math.NT2025

Sums of Laurent series with bounded partial quotients

Dmitry Gayfulin, Erez Nesharim

In 1947 M.Hall proved that every real number is the sum of an integer and two real numbers whose partial quotients are at most $4$ . Later, Cusick proved that every real number is t…

math.NT2024

The shifted fourth moment of modular form L-functions in the weight aspect

Olga Balkanova, Dmitry Frolenkov

We prove a reciprocity type formula for the fourth moment of L-functions associated to holomorphic primitive cusp forms of level one and large weight which relates it to the eighth…

math.NT2023★ 3 cited

A new Andrews--Crandall-type identity and the number of integer solutions to $x^{2} + 2 y^{2} + 2 z^{2} = n$

Mariia Dospolova, Ekaterina Kochetkova, Eric T. Mortenson

Using a higher-dimensional analog of an identity known to Kronecker, we discover a new Andrews--Crandall-type identity and use it to count the number of integer solutions to $x^2+2…

math.NT2023

On Furstenberg's Diophantine result

Dmitry Gayfulin, Nikolay Moshchevitin

We give a very simple and explicit exposition of the effective results on $\times a \times b$ by Bourgain, Lindenstrauss, Michel and Venkatesh.

math.NT2022

A large integer is a sum of two prime avoiding numbers

Artyom Radomskii

Let $f (n) = min_{p} ∣ n - p ∣$ , where $p$ is a prime. We show that there is a positive constant $δ$ such that for any large integer $N$ there exist two positive integers $n_{1}$ and $n_{2}$ …

math.NT2022

On geometry of p-adic polynomials

Evgeny Zelenov

An analogue of the Gauss-Lucas theorem for polynomials over the algebraic closure $C_{p}$ of the field of $p$ -adic numbers is considered.