The local converse theorem for ( Sp)over-tilde2n

Abstract

In this paper, we establish the local converse theorem and the stability of local gamma factors for ( Sp) over tilde (2n) via the precise local theta correspondence between (Sp) over tilde (2n) and SO2n+1 over local fields of characteristic not equal to 2. We also prove the rigidity theorem for irreducible generic cuspidal automorphic representations of ( Sp) over tilde (2n) over number fields.