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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.13062 |
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| _version_ | 1866911512463933440 |
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| author | Di Scipio, Matteo |
| author_facet | Di Scipio, Matteo |
| contents | We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for $κ=2$ and the non-holomorphic case for $m_1m_2<0$. Given two sets of hypothesis on the non archimedean test function $f$, called the geometric and spectral assumptions, this approach allows us to obtain refined PBK formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13062 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The weight two and opposite sign cases for the Fourier relative trace formulas Di Scipio, Matteo Number Theory We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for $κ=2$ and the non-holomorphic case for $m_1m_2<0$. Given two sets of hypothesis on the non archimedean test function $f$, called the geometric and spectral assumptions, this approach allows us to obtain refined PBK formulas. |
| title | The weight two and opposite sign cases for the Fourier relative trace formulas |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.13062 |