On automorphic L-functions in positive characteristic

We give a proof of the existence of Asai, exterior square, and symmetric square local L-functions, γ-factors and root numbers in characteristic p - the case of p = 2 included. Our study is made possible by developing the Langlands-Shahidi method over a global function field in the case of a Siegel Levi subgroup of a split classical group or a quasi-split unitary group. The resulting automorphic L-functions are shown to satisfy a rationality property and a functional equation. A uniqueness result of G. Henniart and the author allows us to show that the definitions provided in this article are in accordance with the local Langlands conjecture for GL_n. Furthermore, in order to be self contained, we include a treatise of L-functions arising from maximal Levi subgroups of general linear groups.