Sums with multiplicative functions over a Beatty sequence

TL;DR

This paper investigates sums involving multiplicative functions over Beatty sequences and derives asymptotic formulas, including counts of integers in such sequences that can be expressed as sums of two squares.

Contribution

It introduces new asymptotic formulas for sums over Beatty sequences involving multiplicative functions, with applications to classical number theory problems.

Findings

Derived asymptotic formulas for sums over Beatty sequences

Applied results to count integers as sums of two squares in Beatty sequences

Extended understanding of multiplicative functions in non-homogeneous sequences

Abstract

We study sums with multiplicative functions that take values over a non-homogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas such as the number of integers in a Beatty sequence representable as a sum of two squares up to a given magnitude.