On the local doubling $\gamma$-factor for classical groups over function fields

Abstract

In this paper, we give a precise definition of an analytic $\gamma$-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough to define it uniquely. We use the doubling method to define the $\gamma$-factor, and the main theorem extends works of Lapid-Rallis, Gan, Yamana, and the author to a classical group over a local function field of odd characteristic.