Twisted Weyl group multiple Dirichlet series over the rational function field

2018/11/02 by Holley Friedlander, Friedlander, Holley
Mathematics · #11M41 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Primary 11F68 #Secondary 11R58 #math.NT #msc:11F68 #msc:11M41 #msc:11R58

paper · pdf · doi:10.48550/arxiv.1811.00988

27 pages, 2 figures

arxiv created 2018/11/02 · openalex publication_date 2018/11/02 · arxiv updated 2018/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weyl group multiple Dirichlet series are Dirichlet series in r complex variables, with analytic continuation to ℂ^r and a group of functional equations isomorphic to the Weyl group of a reduced root system of rank r. Such series may be defined for any global field K, but in the case when K is an algebraic function field they are expected to be, up to a variable change, rational functions in several variables. We verify the rationality of these functions in the case when K=\mathbbF_q(T), and describe the denominators and support of the numerators.

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