The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909924674502656 |
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| author | Peng, Yunjian |
| author_facet | Peng, Yunjian |
| contents | In this paper, we establish the Weyl bound for the Rankin-Selberg $L$-function in a certain joint ramification setting. To achieve this result, we employ the refined Petersson trace formula and develop a special Voronoï summation formula. Additionally, we obtain the sharp bound for the integral of products of Whittaker functions via the $p$-adic stationary phase method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification Peng, Yunjian Number Theory In this paper, we establish the Weyl bound for the Rankin-Selberg $L$-function in a certain joint ramification setting. To achieve this result, we employ the refined Petersson trace formula and develop a special Voronoï summation formula. Additionally, we obtain the sharp bound for the integral of products of Whittaker functions via the $p$-adic stationary phase method. |
| title | The Weyl bound for Rankin-Selberg $L$-functions with Joint Ramification |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.20488 |