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

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.