On the Holomorphy of Exterior-Square L-functions

2011/08/10 by Dustin David Belt, Dustin Belt, Belt, Dustin · 2 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1108.2200

Preprint of Doctoral Dissertation (Purdue University);v.6 due to a mistake that was found in the the previous version, the main result has been weakened a little, but still applies in most applications, 50 pages, 1 appendix

openalex publication_date 2011/08/10 · arxiv created 2012/06/07 · arxiv updated 2012/06/08 · 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
• LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS

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