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arXiv · 2603.13062

The weight two and opposite sign cases for the Fourier relative trace formulas

Matteo Di Scipio
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Abstract

We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for $\kappa=2$ 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.

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Matteo Di Scipio. 2026-03-13. The weight two and opposite sign cases for the Fourier relative trace formulas. https://arxiv.org/abs/2603.13062

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