Translator Disclaimer
May 2020 A Refinement of the Burgess Bound for Character Sums
Bryce Kerr, Igor E. Shparlinski, Kam Hung Yau
Michigan Math. J. 69(2): 227-240 (May 2020). DOI: 10.1307/mmj/1573700737

Abstract

In this paper we give a refinement of the Burgess bound for multiplicative character sums modulo a prime number q. This continues a series of previous logarithmic improvements, which are mostly due to Friedlander, Iwaniec, and Kowalski. In particular, for any nontrivial multiplicative character χ modulo a prime q and any integer r2, we show that M<nM+Nχ(n)=O(N11/rq(r+1)/4r2(logq)1/4r), which sharpens the previous results by a factor (logq)1/4r. Our improvement comes from averaging over numbers with no small prime factors rather than over an interval as in the previous approaches.

Citation

Download Citation

Bryce Kerr. Igor E. Shparlinski. Kam Hung Yau. "A Refinement of the Burgess Bound for Character Sums." Michigan Math. J. 69 (2) 227 - 240, May 2020. https://doi.org/10.1307/mmj/1573700737

Information

Received: 28 February 2018; Revised: 22 April 2019; Published: May 2020
First available in Project Euclid: 14 November 2019

zbMATH: 07244370
MathSciNet: MR4104371
Digital Object Identifier: 10.1307/mmj/1573700737

Subjects:
Primary: 11L40, 11N25

Rights: Copyright © 2020 The University of Michigan

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.69 • No. 2 • May 2020
Back to Top