Constructing Weyl group multiple Dirichlet series

Details Constructing Weyl group multiple Dirichlet series Constructing Weyl group multiple Dirichlet series

2008-03-05

arxiv.org/abs/0803.0691v2

Mathematics

Number Theory

incorporates referee's revisions

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, that has meromorphic continuation to C^r and satisfies functional equations under the transformations of C^r corresponding to the Weyl group of Phi. A heuristic definition of such series was given in [2], and they have been investigated in certain special cases in [2-6, 11-14]. In this paper we generalize results in [13] to construct Weyl group multiple Dirichlet series by a uniform method, and show in all cases that they have the expected properties.

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