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Bibliographic Details
Main Author: Chu, Rena
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2501.12325
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Table of Contents:
  • Let $p$ be a prime. We prove bounds on short Dirichlet character sums evaluated at a class of homogeneous polynomials in arbitrary dimensions. In every dimension, this bound is nontrivial for sums over boxes with side lengths as short as $p^{1/4 + κ}$ for any $κ>0$. Our methods capitalize on the relationship between characters mod $p$ and characters over finite field extensions as well as bounds on the multiplicative energy of sets in products of finite fields.