Séminaire Groupes Réductifs et Formes Automorphes
Alexis Bouthier, Cong Xue
Email des responsables :
Yiannis Sakellaridis - National Technical University of Athens et Rutgers University at Newark,
A "beyond endoscopy" proof of Waldspurger's toric period formula
10:30 à 12:00
I will present a recent proof of Waldspurger's formula relating the square of a period integral of a PGL(2)-automorphic form over a torus to the central value of an L-function. The feature of this proof is a non-standard comparison of relative trace formulas, where scalar transfer factors are replaced by transfer operators. This proof is motivated by very general conjectures about periods and the spectral decomposition of relative trace formulas, which suggest the existence of "relative functoriality" between the trace formulas.