Subconvex bound for Rankin-Selberg $L$-functions in prime power level
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910788916084736 |
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| author | Ghosh, Aritra |
| author_facet | Ghosh, Aritra |
| contents | Let $f$ be a $p$-primitive cusp form of level $p^{4r}$, where local representation of $f$ be supercuspidal at $p$, $p$ being an odd prime, $r\geq 1$ and $g$ be a Hecke-Maass or holomorphic primitive cusp form for $\mathrm{SL}(2,\mathbb{Z})$. A subconvex bound for the central values of the Rankin-Selberg $L$-functions $L(s, f \otimes g )$ is given by $$ L (\frac{1}{2}, f \otimes g ) \ll_{g,ε}p^{\frac{23r}{12} +ε}.$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subconvex bound for Rankin-Selberg $L$-functions in prime power level Ghosh, Aritra Number Theory Let $f$ be a $p$-primitive cusp form of level $p^{4r}$, where local representation of $f$ be supercuspidal at $p$, $p$ being an odd prime, $r\geq 1$ and $g$ be a Hecke-Maass or holomorphic primitive cusp form for $\mathrm{SL}(2,\mathbb{Z})$. A subconvex bound for the central values of the Rankin-Selberg $L$-functions $L(s, f \otimes g )$ is given by $$ L (\frac{1}{2}, f \otimes g ) \ll_{g,ε}p^{\frac{23r}{12} +ε}.$$ |
| title | Subconvex bound for Rankin-Selberg $L$-functions in prime power level |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.01739 |