Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

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• 作者：Ilwoo Cho ; Timothy Gillespie ; Palle E. T. Jorgensen
• 刊名：Analysis and Mathematical Physics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：6
• 期：3
• 页码：255-295
• 全文大小：715 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1664-235X
• 卷排序：6

文摘

In this paper, we study a free-probabilistic model on the algebra of arithmetic functions by considering their asymptotic behavior. As an application, we concentrate on arithmetic functions arising from certain representations attached to the general linear group \(GL_n\). We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.KeywordsArithmetic functionsCuspidal automorphic representations Dirichlet charactersDirichlet seriesp-Adic number fieldsThe adele ringAlgebraic groupsFree momentsFree cumulantsFree probability spaces