Local exterior square and Asai L-functions for GL(n) in odd characteristic

Abstract

Let F be a nonarchimedean local field of odd characteristic p>0. We consider local exterior square L-functions L(s, π, ∧ 2 ), Bump-Friedberg L-functions L(s, π, BF), and Asai L-functions L(s, π, As) of an irreducible admissible representation π of GL m (F). In particular, we establish that those Lfunctions, via the theory of integral representations, are equal to their corresponding Artin L-functions L s, ∧ 2 (φ(π )) , L s + 1 2 , φ(π ) L 2s, ∧ 2 (φ(π )) , and L s, As(φ(π )) of the associated Langlands parameter φ(π ) under the local Langlands correspondence. These are achieved by proving the identity for irreducible supercuspidal representations, exploiting the local-to-global argument due to Henniart and Lomelí.