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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.19649 |
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| _version_ | 1866909577053732864 |
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| author | González, Oscar E. Sun, Qihang |
| author_facet | González, Oscar E. Sun, Qihang |
| contents | Traces of singular moduli can be approximated by exponential sums of quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to estimate generalized twisted traces with power-saving error bounds. We establish an asymptotic formula with effective error bounds for such traces. Our methods depend on an explicit bound for sums of Kloosterman sums on $Γ_0(4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19649 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Effective estimates for traces of singular moduli González, Oscar E. Sun, Qihang Number Theory Traces of singular moduli can be approximated by exponential sums of quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to estimate generalized twisted traces with power-saving error bounds. We establish an asymptotic formula with effective error bounds for such traces. Our methods depend on an explicit bound for sums of Kloosterman sums on $Γ_0(4)$. |
| title | Effective estimates for traces of singular moduli |
| topic | Number Theory |
| url | https://arxiv.org/abs/2305.19649 |