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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| 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.