Improving the Burgess bound via Polya-Vinogradov

2017/06/09 by Fromm, Elijah, Goldmakher, Leo · 1 citation
#11L40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.03002

Abstract

We show that even mild improvements of the Polya-Vinogradov inequality would imply significant improvements of Burgess' bound on character sums. Our main ingredients are a lower bound on certain types of character sums (coming from works of the second author joint with J. Bober and Y. Lamzouri) and a quantitative relationship between the mean and the logarithmic mean of a completely multiplicative function.

Cited by

• Burgess-type character sum estimates over generalized arithmetic progressions of rank 2

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