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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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| _version_ | 1866918258078121984 |
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| author | Chu, Rena |
| author_facet | Chu, Rena |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates for short character sums evaluated at homogeneous polynomials Chu, Rena Number Theory 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. |
| title | Estimates for short character sums evaluated at homogeneous polynomials |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.12325 |