Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912574784667648 |
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| author | Xu, Zhao |
| author_facet | Xu, Zhao |
| contents | In this paper, we study the second moment for $GL(2)\times GL(2)$ $L$-functions $L(\frac{1}{2},f\times g)$, which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either $f$ or $g$ is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both $t_f$ and $t_g$, where $t_f$, $t_g$ denote the spectral parameters of $f$, $g$. As an application, we also establish a shrinking result for QUE in the case of dihedral Maass newforms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect Xu, Zhao Number Theory 11F12, 11F66, 11F72 In this paper, we study the second moment for $GL(2)\times GL(2)$ $L$-functions $L(\frac{1}{2},f\times g)$, which leads to a uniform subconvexity bound in the spectral aspect. In particular, if either $f$ or $g$ is a dihedral Maass newform, or if one of them has level $1$, we obtain a Burgess-type bound that is uniform in both $t_f$ and $t_g$, where $t_f$, $t_g$ denote the spectral parameters of $f$, $g$. As an application, we also establish a shrinking result for QUE in the case of dihedral Maass newforms. |
| title | Uniform subconvexity bounds for $GL(2)\times GL(2)$ $L$-functions in the spectral aspect |
| topic | Number Theory 11F12, 11F66, 11F72 |
| url | https://arxiv.org/abs/2509.05968 |