Gamma factors and converse theorems for classical groups over finite fields

Abstract

In this paper, we prove certain multiplicity one theorems and define GL-twisted gamma factors for irreducible generic cuspidal representations of quasi-split classical groups Gr=Sp2r,U2r, U2r+1,SO2r+1 over finite fields of odd characteristic, using Rankin-Selberg method. As applications, we prove converse theorems for these groups, namely, GLn-twisted gamma factors, n=1,2,…,r, will uniquely determine irreducible generic cuspidal representations of Gr(Fq).