Affine Weyl group multiple Dirichlet series: type
نویسندگان
چکیده
منابع مشابه
Weyl Group Multiple Dirichlet Series of Type C
We develop the theory of “Weyl group multiple Dirichlet series” for root systems of type C. For a root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and functional equations isomorphic to the associated Weyl group. They conjecturally arise as Whittaker coefficients of Eisenstein series on a metaplectic group with cover de...
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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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Preface An L-function, as the term is generally understood, is a Dirichlet series in one complex variable s with an Euler product that has (at least conjecturally) analytic continuation to all complex s and a functional equation under a single reflection s → 1 − s. The coefficients are in particular multiplicative. By contrast Weyl group multiple Dirichlet series are a new class of Dirichlet se...
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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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This paper describes a technique to construct Weyl group multiple Dirichlet series. Such series were first introduced in [BBC06], which also described a heuristic means to define, analytically continue, and prove functional equations for a family of Dirichlet series in several complex variables. Several subsequent papers have dealt with the problem of making the heuristic definitions precise an...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2016
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x16007715