Quartic Gauss sums over primes and metaplectic theta functions
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917233510318080 |
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| author | David, Chantal Dunn, Alexander Hamieh, Alia Lin, Hua |
| author_facet | David, Chantal Dunn, Alexander Hamieh, Alia Lin, Hua |
| contents | We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares. We also conjecture asymptotics for certain moments of quartic Gauss sums over primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11875 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quartic Gauss sums over primes and metaplectic theta functions David, Chantal Dunn, Alexander Hamieh, Alia Lin, Hua Number Theory 11F27, 11F30, 11L05, 11L20, 11N36 We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over $\mathbb{Q}(i)$, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta functions at squares. We also conjecture asymptotics for certain moments of quartic Gauss sums over primes. |
| title | Quartic Gauss sums over primes and metaplectic theta functions |
| topic | Number Theory 11F27, 11F30, 11L05, 11L20, 11N36 |
| url | https://arxiv.org/abs/2306.11875 |