Difference sets and positive exponential sums I. General properties

TL;DR

This paper explores the relationship between difference sets in Abelian groups and positive exponential sums, establishing connections that relate the size of certain sets to exponential sum properties.

Contribution

It introduces general connections between intersective properties of sets and positive exponential sums in Abelian groups, providing a theoretical framework.

Findings

Relation between difference set sizes and exponential sums

Connections between intersective properties and exponential sums

Theoretical insights into Abelian group set properties

Abstract

We describe general connections between intersective properties of sets in Abelian groups and positive exponential sums. In particular, given a set $A$ the maximal size of a set whose difference set avoids $A$ will be related to positive exponential sums using frequencies from $A$.