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Unitary Friedberg-Jacquet periods and their twists: Relative trace formulas
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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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Bump-Friedberg type periods beyond the cuspidal spectrum
Bump–Friedberg-type periods extend continuously beyond the cuspidal spectrum under regularity, and on GL_{2n+1} Eisenstein series they equal a sum of L-values indexed by dual-variety fixed points.
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