Automorphic descent for symplectic groups: The branching problems and L -functions

Abstract

We study certain automorphic descent constructions for symplectic groups, and obtain results related to branching problems of automorphic representations. As a byproduct of the construction, based on the knowledge of the global Vogan packets for ${\rm Mp}_2(\Bbb{A})$, we give a new approach to prove the result that for an automorphic cuspidal representation of ${\rm GL}_2(\Bbb{A})$ of symplectic type, if there exists a quadratic twist with positive root number, then there exist quadratic twists with non-zero central $L$-values.