2025/03/12 by Spencer Leslie, Leslie, Spencer, Xiao Jingwei +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Crystallography and Radiation Phenomena #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2503.09500
openalex publication_date 2025/03/12 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28
We formulate 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 GL(2). We introduce a new relative trace formula to prove our global conjecture under some local hypotheses. A new feature is the presence of the relative endoscopy. In this paper we prove the main local theorem: a new relative fundamental lemma comparing certain orbital integrals of functions matched in terms of Hironaka and Satake transforms.