Burgess bounds for multi-dimensional short mixed character sums
Journal Article (Journal Article)
This paper proves Burgess bounds for short mixed character sums in multi-dimensional settings. The mixed character sums we consider involve both an exponential evaluated at a real-valued multivariate polynomial f, and a product of multiplicative Dirichlet characters. We combine a multi-dimensional Burgess method with recent results on multi-dimensional Vinogradov Mean Value Theorems for translation-dilation invariant systems in order to prove character sum bounds in k≥ 1 dimensions that recapture the Burgess bound in dimension 1. Moreover, we show that by embedding any given polynomial f into an advantageously chosen translation-dilation invariant system constructed in terms of f, we may in many cases significantly improve the bound for the associated character sum, due to a novel phenomenon that occurs only in dimensions k≥ 2.
Full Text
Duke Authors
Cited Authors
- Pierce, LB
Published Date
- June 1, 2016
Published In
Volume / Issue
- 163 /
Start / End Page
- 172 - 210
International Standard Serial Number (ISSN)
- 0022-314X
Digital Object Identifier (DOI)
- 10.1016/j.jnt.2015.08.022
Citation Source
- Scopus