Character sums to prime power moduli evaluated at binary quadratic forms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911686461489152 |
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| author | Baier, Stephan Chattopadhyay, Aishik |
| author_facet | Baier, Stephan Chattopadhyay, Aishik |
| contents | We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character sums to squarefree moduli. Our approach uses $p$-adic analysis. More precisely, we use tools from the $p$-adic theory of exponential sums, as initiated by Milićević. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11231 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Character sums to prime power moduli evaluated at binary quadratic forms Baier, Stephan Chattopadhyay, Aishik Number Theory 11L40, 11T24, 11L07, 11E08 We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character sums to squarefree moduli. Our approach uses $p$-adic analysis. More precisely, we use tools from the $p$-adic theory of exponential sums, as initiated by Milićević. |
| title | Character sums to prime power moduli evaluated at binary quadratic forms |
| topic | Number Theory 11L40, 11T24, 11L07, 11E08 |
| url | https://arxiv.org/abs/2508.11231 |