Sums of multiplicative characters with additive convolutions

TL;DR

This paper provides new bounds for sums involving multiplicative characters and additive convolutions of sets with small doubling, improving previous results using the Croot-Sisask almost periodicity lemma.

Contribution

It introduces improved estimates for character sums with additive convolutions, advancing the understanding of their behavior in sets with small additive doubling.

Findings

Enhanced bounds for binary and ternary sums of multiplicative characters

Application of Croot-Sisask lemma to additive convolution estimates

Improvement over previous results by M.-C. Chang

Abstract

In the paper we obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets, having small additive doubling. In particular, we improve a result of M.-C. Chang. The proof uses Croot-Sisask almost periodicity lemma.