On holomorphy of local Langlands L-functions

Mahdi Asgari, Purdue University

Abstract

This work studies local Langlands L-functions defined via the Langlands-Shahidi method which associates a complex function with a generic representation of a Levi subgroup in a quasi-split reductive p-adic group. Defining these functions via existence of certain γ-factors, essentially quotients of these L-functions, Shahidi set forth a conjecture on their holomorphy in a half plane if the representation is tempered. He subsequently proved this conjecture for classical groups. The goal here is to prove this conjecture for Levi subgroups of the so-called spin groups, the double coverings of special orthogonal groups. We also verify the conjecture for Levi subgroups of exceptional groups of type F 4. H. Kim has recently proved the conjecture for E-type exceptional groups except for a few cases in which the representation theory of the Levi subgroup is not known well enough. The conjecture for an exceptional group of type G2 is already well-known.

Degree

Ph.D.

Advisors

Shahidi, Purdue University.

Subject Area

Mathematics

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