Character sums over Bohr sets

TL;DR

This paper establishes bounds on character sums over additive Bohr sets modulo a prime, extending classical results and applying them to recurrence problems in modular arithmetic.

Contribution

It introduces new character sum estimates for Bohr sets, analogous to classical bounds, and applies these to recurrence phenomena in modular settings.

Findings

Derived bounds similar to Polya-Vinogradov and Burgess for Bohr sets

Applied estimates to recurrence problems modulo prime

Extended classical character sum bounds to new algebraic structures

Abstract

We prove character sum estimates for additive Bohr subsets modulo a prime. These estimates are analogous to classical character sum bounds of Polya-Vinogradov and Burgess. These estimates are applied to obtain results on recurrence mod $p$ by special elements.