Weyl group multiple Dirichlet series of typeC
نویسندگان
چکیده
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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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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If F is a local field containing the group μn of n-th roots of unity, and if G is a split semisimple simply connected algebraic group, then Matsumoto [27] defined an n-fold covering group of G(F ), that is, a central extension of G(F ) by μn. Similarly if F is a global field with adele ring AF containing μn there is a cover G̃(AF ) of G(AF ) that splits over G(F ). The construction is built on i...
متن کاملWeyl Group Multiple Dirichlet
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...
متن کاملWeyl 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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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2011
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2011.254.11