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Weyl group multiple Dirichlet series of type A_2

Gautam Chinta·Paul E. Gunnells
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Abstract

A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Phi. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n-th order Gauss sums attached to the root system of type A_2. The basic technique is to construct a rational function in r variables invariant under a certain action of W, and use this to build a ``local factor'' of the global series.

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Gautam Chinta, Paul E. Gunnells. 2007-03-01. Weyl group multiple Dirichlet series of type A_2. https://arxiv.org/abs/math/0703040

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