Constructing Weyl Group Multiple Dirichlet
نویسنده
چکیده
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 [2], and they have been investigated in certain special cases in [2–6, 11–14]. In this paper we generalize results in [13] to construct Weyl group multiple Dirichlet series by a uniform method, and show in all cases that they have the expected properties.
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m at h . N T ] 1 4 M ay 2 00 9 CONSTRUCTING WEYL GROUP MULTIPLE DIRICHLET SERIES
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 [BB...
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