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Weyl group multiple Dirichlet series II: The stable case

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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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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305-2125, USA

    Ben Brubaker & Daniel Bump

  2. Department of Mathematics, Boston College, Chestnut Hill, MA, 02467-3806, USA

    Solomon Friedberg

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  1. Ben Brubaker
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  2. Daniel Bump
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  3. Solomon Friedberg
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Brubaker, B., Bump, D. & Friedberg, S. Weyl group multiple Dirichlet series II: The stable case. Invent. math. 165, 325–355 (2006). https://doi.org/10.1007/s00222-005-0496-2

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