Rank Lowering Linear Maps and Multiple Dirichlet Series Associated to GL(n,R)
نویسندگان
چکیده
منابع مشابه
Multiple Dirichlet Series
This introductory article aims to provide a roadmap to many of the interrelated papers in this volume and to a portion of the field of multiple Dirichlet series, particularly emerging new ideas. It is both a survey of the recent literature, and an introduction to the combinatorial aspects of Weyl group multiple Dirichlet series, a class of multiple Dirichlet series that are not Euler products, ...
متن کاملIntroduction: Multiple Dirichlet Series
This introductory article aims to provide a roadmap to many of the interrelated papers in this volume and to a portion of the field of multiple Dirichlet series, particularly emerging new ideas. It is both a survey of the recent literature, and an introduction to the combinatorial aspects of Weyl group multiple Dirichlet series, a class of multiple Dirichlet series that are not Euler products, ...
متن کاملDirichlet Series for Finite Combinatorial Rank Dynamics
We introduce a class of group endomorphisms – those of finite combinatorial rank – exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to to be a rational function of exponential variables. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on th...
متن کاملMultiple Dirichlet Series and Automorphic Forms
This article gives an introduction to the multiple Dirichlet series arising from sums of twisted automorphic L-functions. We begin by explaining how such series arise from Rankin-Selberg constructions. Then more recent work, using Hartogs’ continuation principle as extended by Bochner in place of such constructions, is described. Applications to the nonvanishing of Lfunctions and to other probl...
متن کاملWeyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
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...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2006
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2006.v2.n2.a10