Constructing Weyl group multiple Dirichlet series

By Gautam Chinta, Paul E. Gunnells. 2008

87 citations recorded by the source corpus.

Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for Re(si) sufficiently large, that has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. A heuristic definition of such series was given in [BBC06], and they have been investigated in certain special cases in [BBC06,BBF06,BBFH07, BBF08, BBFa, CG07, CFG08, CG, Chi05]. In this paper we generalize results in [CG] to construct Weyl group multiple Dirichlet series by a uniform method, and show in all cases that they have the expected properties.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe38f7ca441805d3d28a09bb8cb798e24e52a123

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Citations in the corpus

Multiple Dirichlet series, L-functions and automorphic forms (2012, background): “The first of these is expressed in terms of a Weyl group action described in [10], 1991 Mathematics Subject Classification.”
Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (2011, methodology): “At this writing, the crystal graph approach can be used to define Weyl group multiple Dirichlet series for Type C r (with n odd) as in Beineke, Brubaker and Frechette [1] and in Type B r (with n even) as in Brubaker, Bump, Chinta and Gunnells [5] whose conjectured analytic properties can be proved i”