Weyl group multiple Dirichlet series II: The stable case
成果类型：
Article
署名作者：
Brubaker, Ben; Bump, Daniel; Friedberg, Solomon
署名单位：
Stanford University; Boston College
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-005-0496-2
发表日期：
2006
页码：
325-355
关键词：
摘要：
To each reduced root system Phi 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 Phi. 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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