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Weyl Group Multiple Dirichlet Series by Ben Brubaker, Daniel Bump, Solomon Friedberg

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Chapter One

Type A Weyl Group Multiple Dirichlet Series

We begin by defining the basic shape of the class of Weyl group multiple Dirichlet series. To do so, we choose the following parameters.

  • Φ, a reduced root system. Let r denote the rank of Φ.
  • n, a positive integer,
  • F, an algebraic number field containing the group μ2n of 2n-th roots of unity,
  • S, a finite set of places of F containing all the archimedean places, all places ramified over Image, and large enough so that the ring

    ImageS = {x ∈ F | |x|υ 1 for υ S}

    of S-integers is a principal ideal domain, ...

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