Uniform bounds for Kloosterman sums of half-integral weight, same-sign case
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912322784591872 |
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| author | Sun, Qihang |
| author_facet | Sun, Qihang |
| contents | In the previous paper [Sun23], the author proved a uniform bound for sums of half-integral weight Kloosterman sums. This bound was applied to prove an exact formula for partitions of rank modulo 3. That uniform estimate provides a more precise bound for a certain class of multipliers compared to the 1983 result by Goldfeld and Sarnak and generalizes the 2009 result from Sarnak and Tsimerman to the half-integral weight case. However, the author only considered the case when the parameters satisfied $\tilde m\tilde n<0$. In this paper, we prove the same uniform bound when $\tilde m\tilde n>0$ for further applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05233 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform bounds for Kloosterman sums of half-integral weight, same-sign case Sun, Qihang Number Theory 11L05, 11F37 In the previous paper [Sun23], the author proved a uniform bound for sums of half-integral weight Kloosterman sums. This bound was applied to prove an exact formula for partitions of rank modulo 3. That uniform estimate provides a more precise bound for a certain class of multipliers compared to the 1983 result by Goldfeld and Sarnak and generalizes the 2009 result from Sarnak and Tsimerman to the half-integral weight case. However, the author only considered the case when the parameters satisfied $\tilde m\tilde n<0$. In this paper, we prove the same uniform bound when $\tilde m\tilde n>0$ for further applications. |
| title | Uniform bounds for Kloosterman sums of half-integral weight, same-sign case |
| topic | Number Theory 11L05, 11F37 |
| url | https://arxiv.org/abs/2309.05233 |