LOCAL EXTERIOR SQUARE AND ASAI L-FUNCTIONS FOR GL(n) IN ODD CHARACTERISTIC

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 (Formula Presented) 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.