On the p-parts of quadratic Weyl group multiple Dirichlet series
Gautam Chinta, Solomon Friedberg, Paul E. Gunnells
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,...,sr, initially converging for Re(si) sufficiently large, which has meromorphic continuation to Cr and satisfies functional equations under the transformations of Cr 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=Ar they yield the same multiple Dirichlet series.
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