Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$-functions II
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910562911256576 |
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| author | Frolenkov, Dmitry |
| author_facet | Frolenkov, Dmitry |
| contents | We prove an asymptotic formula for $F\left(1/4-it+ir,1/4-it-ir,1/2;x \right)$ as $r, t\to\infty$ and $α=r/t\to0.$ This special case of the Gauss hypergeometric function appears in the explicit formula for the first moment of Maass form symmetric-square $L$-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$-functions II Frolenkov, Dmitry Number Theory 33C05, 41A60 We prove an asymptotic formula for $F\left(1/4-it+ir,1/4-it-ir,1/2;x \right)$ as $r, t\to\infty$ and $α=r/t\to0.$ This special case of the Gauss hypergeometric function appears in the explicit formula for the first moment of Maass form symmetric-square $L$-functions. |
| title | Asymptotics of a Gauss hypergeometric function related to moments of symmetric-square $L$-functions II |
| topic | Number Theory 33C05, 41A60 |
| url | https://arxiv.org/abs/2408.05619 |