Endoscopic congruences modulo adjoint L-values for GSp(4)

Abstract

. We establish the existence of congruences between a fixed endoscopic, globally generic, cuspidal automorphic representation Π of GSp(4) of square-free conductor and stable cuspidal automorphic representations of the same weight modulo certain prime factors of the value at 1 of the adjoint L -function of Π normalized by a suitable period.