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arXiv · 1811.00988

Twisted Weyl group multiple Dirichlet series over the rational function field

Holley Friedlander
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Abstract

Weyl group multiple Dirichlet series are Dirichlet series in $r$ complex variables, with analytic continuation to $\mathbb{C}^r$ and a group of functional equations isomorphic to the Weyl group of a reduced root system of rank $r$. Such series may be defined for any global field $K$, but in the case when $K$ is an algebraic function field they are expected to be, up to a variable change, rational functions in several variables. We verify the rationality of these functions in the case when $K=\mathbb{F}_q(T)$, and describe the denominators and support of the numerators.

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Holley Friedlander. 2018-11-02. Twisted Weyl group multiple Dirichlet series over the rational function field. https://arxiv.org/abs/1811.00988

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