Inventiones mathematicae

, Volume 165, Issue 2, pp 325–355 | Cite as

Weyl group multiple Dirichlet series II: The stable case

  • Ben Brubaker
  • Daniel Bump
  • Solomon Friedberg


To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Ben Brubaker
    • 1
  • Daniel Bump
    • 1
  • Solomon Friedberg
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsBoston CollegeChestnut HillUSA

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