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arXiv · 2503.09664

Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas

Spencer Leslie·Jingwei Xiao·Wei Zhang
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Abstract

In a companion paper, we formulated a global conjecture for the automorphic period integral associated to the symmetric pairs defined by unitary groups over number fields, generalizing a theorem of Waldspurger's toric period for $\mathrm{GL}(2)$. In this paper, we introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of relative endoscopy in the comparison. We also establish several local results on relative characters.

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Spencer Leslie, Jingwei Xiao, Wei Zhang. 2025-03-12. Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas. https://arxiv.org/abs/2503.09664

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