Character sums to smooth moduli are small
by
Leo Goldmakher
University of Michigan / Stanford University

Recently, Granville and Soundararajan have shown that a primitive character sum can be large if and only if the character 'pretends' to be like a primitive character of small conductor and opposite parity. From this characterization they were able to deduce a number of new results, including an improvement of the Polya-Vinogradov inequality for characters of bounded odd order. In this talk I will briefly describe their work and demonstrate how their characterization can be applied to improve Polya-Vinogradov for characters to smooth moduli.

Date received: May 20, 2008