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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18088 |
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| _version_ | 1866911222990897152 |
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| author | Dobrowolski, Jakub |
| author_facet | Dobrowolski, Jakub |
| contents | We prove an asymptotic formula with a power-saving error term for a specific weighted second moment of $\mathrm{GL}(2)\times \mathrm{GL}(2)$ Rankin-Selberg $L$-function, $L(1/2,π\otimes π_0)$ over any number field $F$ where $π$ runs over representations with the non-archimedean conductor dividing an ideal which tends to infinity and $π_0$ is a fixed cuspidal representation unramified everywhere. The error term shows the square root cancellation under the assumption of the Generalised Ramanujan Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The second moment of $\mathrm{GL}(2)\times \mathrm{GL}(2)$ Rankin-Selberg $L$-functions in the level aspect Dobrowolski, Jakub Number Theory We prove an asymptotic formula with a power-saving error term for a specific weighted second moment of $\mathrm{GL}(2)\times \mathrm{GL}(2)$ Rankin-Selberg $L$-function, $L(1/2,π\otimes π_0)$ over any number field $F$ where $π$ runs over representations with the non-archimedean conductor dividing an ideal which tends to infinity and $π_0$ is a fixed cuspidal representation unramified everywhere. The error term shows the square root cancellation under the assumption of the Generalised Ramanujan Conjecture. |
| title | The second moment of $\mathrm{GL}(2)\times \mathrm{GL}(2)$ Rankin-Selberg $L$-functions in the level aspect |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.18088 |