Hybrid subconvexity for Maass form symmetric-square $L$-functions
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arXiv
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| Format: | Preprint |
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2024
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| author | Balkanova, Olga Frolenkov, Dmitry |
| author_facet | Balkanova, Olga Frolenkov, Dmitry |
| contents | Recently R. Khan and M. Young proved a mean Lindelöf estimate for the second moment of Maass form symmetric-square $L$-functions $L(\text{sym}^2 u_{j},1/2+it)$ on the short interval of length $G\gg |t_j|^{1+ε}/t^{2/3}$, where $t_j$ is a spectral parameter of the corresponding Maass form. Their estimate yields a subconvexity estimate for $L(\text{sym}^2 u_{j},1/2+it)$ as long as $|t_j|^{6/7+δ} \ll t<(2-δ)|t_j|$. We obtain a mean Lindelöf estimate for the same moment in shorter intervals, namely for $G\gg |t_j|^{1+ε}/t$. As a corollary, we prove a subconvexity estimate for $L(\text{sym}^2 u_{j},1/2+it)$ on the interval $|t_j|^{2/3+δ}\ll t\ll |t_j|^{6/7-δ}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid subconvexity for Maass form symmetric-square $L$-functions Balkanova, Olga Frolenkov, Dmitry Number Theory Recently R. Khan and M. Young proved a mean Lindelöf estimate for the second moment of Maass form symmetric-square $L$-functions $L(\text{sym}^2 u_{j},1/2+it)$ on the short interval of length $G\gg |t_j|^{1+ε}/t^{2/3}$, where $t_j$ is a spectral parameter of the corresponding Maass form. Their estimate yields a subconvexity estimate for $L(\text{sym}^2 u_{j},1/2+it)$ as long as $|t_j|^{6/7+δ} \ll t<(2-δ)|t_j|$. We obtain a mean Lindelöf estimate for the same moment in shorter intervals, namely for $G\gg |t_j|^{1+ε}/t$. As a corollary, we prove a subconvexity estimate for $L(\text{sym}^2 u_{j},1/2+it)$ on the interval $|t_j|^{2/3+δ}\ll t\ll |t_j|^{6/7-δ}$. |
| title | Hybrid subconvexity for Maass form symmetric-square $L$-functions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.06735 |