Vol. 14, No. 7, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Burgess bounds for short character sums evaluated at forms

Lillian B. Pierce and Junyan Xu

Vol. 14 (2020), No. 7, 1911–1951
Abstract

We establish a Burgess bound for short multiplicative character sums in arbitrary dimensions, in which the character is evaluated at a homogeneous form that belongs to a very general class of “admissible” forms. This n-dimensional Burgess bound is nontrivial for sums over boxes of sidelength at least qβ, with β > 12 1(2(n + 1)). This is the first Burgess bound that applies in all dimensions to generic forms of arbitrary degree. Our approach capitalizes on a recent stratification result for complete multiplicative character sums evaluated at rational functions, due to the second author.

Keywords
character sums
Mathematical Subject Classification 2010
Primary: 11L40
Milestones
Received: 17 July 2019
Revised: 14 December 2019
Accepted: 6 February 2020
Published: 18 August 2020
Authors
Lillian B. Pierce
Duke University
Durham, NC
United States
Junyan Xu
Indiana University
Bloomington, IN
United States