On automorphic L-functions in positive characteristic

Mathematics – Number Theory

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appendix by G. Henniart and L. A. Lomel\'i

Scientific paper

In this paper, we develop 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. In particular, exterior square, symmetric square, Asai L-functions, and related local factors, are defined and shown to satisfy a functional equation. Previous work of the author with G. Henniart gives a characterization of local factors that enables us to show that the definitions given in this article are in accordance with the local Langlands conjecture for GL(n). In addition, we give a treatise of Rankin-Selberg products of GL(m) and GL(n) in a self contained manner within the LS method. The appendix, written with G. Henniart, gives a proof of a uniqueness result for Rankin-Selberg \gamma-factors. We use this to show equality of local L-functions and root numbers when they are defined via different methods.

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