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

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

2006-12-20

arxiv.org/abs/math/0612595v1

Mathematics

Number Theory

Scientific paper

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 s_1,...,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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