The multiple Dirichlet product and the multiple Dirichlet series
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 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 کاملGeneralized multiple Dirichlet series and generalized multiple polylogarithms
where t is a complex variable. By Assumption I, we see that the series (1.3) is convergent when <t < 0. We further assume the following: (Assumption II ) ψ(s) can be continued analytically to the whole complex plane C, and holomorphic for all s ∈ C. In any fixed strip σ1 ≤ σ ≤ σ2, ψ(s; u) is uniformly convergent to ψ(s) as u → 1 + 0. Furthermore there exists a certain θ0 = θ0(σ1, σ2) ∈ R with 0...
متن کاملMultiple Dirichlet Series over Rational Function Fields
We explicitly compute some double Dirichlet series constructed from n order Gauss sums over rational function fields. These turn out to be rational functions in q−s1 and q−s2 , where q is the size of the constant field. Key use is made of the group of 6 functional equations satisfied by these series.
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042117501184