Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915708351283200 |
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| author | Alsetri, Ali Shao, Xuancheng |
| author_facet | Alsetri, Ali Shao, Xuancheng |
| contents | We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank $2$ in prime fields $\mathbb{F}_p$. The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$ Alsetri, Ali Shao, Xuancheng Number Theory 11L40, 11B30 We extend the classical Burgess estimates to character sums over proper generalized arithmetic progressions (GAPs) of rank $2$ in prime fields $\mathbb{F}_p$. The core of our proof is a sharp upper bound for the multiplicative energy of these sets, established by adapting an argument of Konyagin and leveraging tools from the geometry of numbers. A key step in our argument involves establishing new upper bounds for the sizes of Bohr sets, which may be of independent interest. |
| title | Burgess-type character sum estimates over generalized arithmetic progressions of rank $2$ |
| topic | Number Theory 11L40, 11B30 |
| url | https://arxiv.org/abs/2509.07765 |