# Burgess bounds for multi-dimensional short mixed character sums

```@article{Pierce2014BurgessBF,
title={Burgess bounds for multi-dimensional short mixed character sums},
author={L. Pierce},
journal={arXiv: Number Theory},
year={2014}
}```
• L. Pierce
• Published 2014
• Mathematics
• arXiv: Number Theory
• 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, 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 any dimension that recapture… CONTINUE READING
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