Character sums to smooth moduli are small

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.

18 pages. Section 5 significantly revised

Cited by in corpus (3)

• The distribution of the maximum of character sums
• Burgess bounds for short character sums evaluated at forms
• The Elliott-Halberstam conjecture implies the Vinogradov least quadratic nonresidue conjecture