Inventiones mathematicae

, Volume 165, Issue 2, pp 325–355

Weyl group multiple Dirichlet series II: The stable case


  • Ben Brubaker
    • Department of MathematicsStanford University
  • Daniel Bump
    • Department of MathematicsStanford University
  • Solomon Friedberg
    • Department of MathematicsBoston College

DOI: 10.1007/s00222-005-0496-2

Cite this article as:
Brubaker, B., Bump, D. & Friedberg, S. Invent. math. (2006) 165: 325. doi:10.1007/s00222-005-0496-2


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.

Copyright information

© Springer-Verlag 2006