On the Holomorphy of Exterior-Square L-functions

2011/08/10 by Dustin David Belt, Belt, Dustin · 1 citation
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1108.2200

openalex publication_date 2011/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the twisted partial exterior-square L-function has a meromorphic continuation to the whole complex plane with only two possible simple poles at s=1 and s=0. We do this by establishing the nonvanishing of the local zeta integrals defined by Jacquet and Shalika for any fixed s₀. The even case is treated in detail. The odd case is treated briefly, in which case, the L-function is shown to be entire.

Citations

• On Certain L-Functions

Cited by

• Derivatives and Exceptional Poles of the Local Exterior Square L-Function for GL_m

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