Character sums to smooth moduli are small

TL;DR

This paper improves bounds on character sums for smooth moduli by building on recent breakthroughs and existing estimates, enhancing the classical Polya-Vinogradov inequality.

Contribution

It advances the understanding of character sums for smooth moduli by refining the Polya-Vinogradov inequality using recent and classical estimates.

Findings

Improved bounds on character sums for smooth moduli.

Enhanced the classical Polya-Vinogradov inequality.

Utilized recent breakthroughs and classical estimates to achieve these improvements.

Abstract

Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham-Ringrose and Iwaniec, we improve the Polya-Vinogradov inequality for characters with smooth conductor.