Weyl Group Multiple Dirichlet
نویسنده
چکیده
Abstract. A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Φ. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Φ. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n order Gauss sums attached to the root system of type A2. The basic technique is that of [8, 9]; namely, we construct a rational function in r variables invariant under a certain action of W , and use this to build a “local factor” of the global series.
منابع مشابه
Weyl Group Multiple Dirichlet Series I
Given a root system Φ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums. It is a function of r complex variables, and it has meromorphic continuation to all of C, with functional equations forming a group isomorphic to the Weyl group of Φ. Weyl group multiple Dirichlet s...
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A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Φ. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Φ. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n order Gauss sum...
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