Weyl group multiple Dirichlet series II: The stable case

Ben Brubaker, Daniel Bump, Solomon Friedberg

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)325-355
Number of pages31
JournalInventiones Mathematicae
Issue number2
StatePublished - Aug 1 2006


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