On the p-parts of quadratic Weyl group multiple Dirichlet series

2006/12/20 by Gautam Chinta, Chinta, Gautam, Solomon Friedberg +3
Mathematics · #11F66 #11M41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F66 #msc:11M41

paper · pdf · doi:10.48550/arxiv.math/0612595

arxiv created 2006/12/20 · arxiv updated 2009/12/01

Abstract

Let Phi be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Phi is a Dirichlet series in r complex variables s₁,...,s_r, initially converging for Re(s_i) sufficiently large, which has meromorphic continuation to C^r and satisfies functional equations under the transformations of C^r corresponding to the Weyl group of Phi. Two constructions of such series are available, one based on summing products of n-th order Gauss sums, the second based on averaging a certain group action over the Weyl group. In this paper we study these constructions and the relationship between them, and give evidence that when n=2 and Phi=A_r they yield the same multiple Dirichlet series.

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