On a converse theorem for $G_2$ over finite fields

Abstract

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, $G{L}_1$ and $G{L}_2$-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of $G_2(k)$.

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