The Kloosterman circle method and weighted representation numbers of quadratic forms
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915466363011072 |
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| author | Jones, Edna |
| author_facet | Jones, Edna |
| contents | We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of nonsingular integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, Salié sums, and a principle of nonstationary phase. We briefly discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Kloosterman circle method and weighted representation numbers of quadratic forms Jones, Edna Number Theory 11D85 (Primary) 11D09, 11P55, 11D72 (Secondary) We develop a version of the Kloosterman circle method with a bump function that is used to provide asymptotics for weighted representation numbers of nonsingular integral quadratic forms. Unlike many applications of the Kloosterman circle method, we explicitly state some constants in the error terms that depend on the quadratic form. This version of the Kloosterman circle method uses Gauss sums, Kloosterman sums, Salié sums, and a principle of nonstationary phase. We briefly discuss a potential application of this version of the Kloosterman circle method to a proof of a strong asymptotic local-global principle for certain Kleinian sphere packings. |
| title | The Kloosterman circle method and weighted representation numbers of quadratic forms |
| topic | Number Theory 11D85 (Primary) 11D09, 11P55, 11D72 (Secondary) |
| url | https://arxiv.org/abs/2412.01780 |