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# On automorphic L-functions in positive characteristic

## Resumen

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.

Autores: Lomelí, L. A.

Journal: Annales de l'Institut Fourier

Journal Volume: 66

Journal Issue: 5

Journal Page: 1733-1771

Tipo de publicación: ISI

Fecha de publicación: 2016

Topics: Automorphic L-functions, functional equation, Langlands-Shahidi method, local factors

URL de la publicación: http://aif.cedram.org/cedram-bin/article/AIF_2016__66_5_1733_0.pdf

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