Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

被引：1

作者：

Cho, Ilwoo ^{[1
]}

Gillespie, Timothy ^{[2
]}

Jorgensen, Palle E. T. ^{[3
]}

机构：

[1] St Ambrose Univ, Dept Math, 418 Ambrose Hall,518 W Locust St, Davenport, IA 52803 USA

[2] St Ambrose Univ, Dept Math, 421 Ambrose Hall,518 W Locust St, Davenport, IA 52803 USA

[3] 14 McLean Hall, Iowa City, IA 52242 USA

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2016年 / 6卷 / 03期

基金：

以色列科学基金会;

关键词：

Arithmetic functions; Cuspidal automorphic representations; Dirichlet characters; Dirichlet series; p-Adic number fields; The adele ring; Algebraic groups; Free moments; Free cumulants; Free probability spaces; DYNAMICAL-SYSTEMS;

D O I：

10.1007/s13324-015-0117-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 . We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness.

引用

页码：255 / 295

页数：41

共 43 条

[31] Weighted Selberg orthogonality and uniqueness of factorization of automorphic L-functions [J].

Liu, JY ;

Ye, YB .

FORUM MATHEMATICUM, 2005, 17 (03) :493-512

[32]

Nathanson M. B., 1996, GRAD TEXT IN MATH, V164

[33]

Newman D. J., 1998, GRAD TEXT IN MATH, V177

[34]

Nica Alexandru, 2006, Lectures on the combinatorics of free probability, V13

[35]

Phillips R. S., 1961, PROC INTERNAT SYMPOS, P366

[36] RANDOM MATRICES, AMALGAMATED FREE-PRODUCTS AND SUBFACTORS OF THE VON-NEUMANN ALGEBRA OF A FREE GROUP, OF NONINTEGER INDEX [J].

RADULESCU, F .

INVENTIONES MATHEMATICAE, 1994, 115 (02) :347-389

[37] Dirichlet expression for L(1, χ) with general Dirichlet character [J].

Rane, V. V. .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2010, 120 (01) :7-9

[38]

Rogalwski E., 1997, Proceedings of Symposia in Pure Mathematics, V61, P331

[39] Zeros of principal L-functions and random matrix theory [J].

Rudnick, Z ;

Sarnak, P .

DUKE MATHEMATICAL JOURNAL, 1996, 81 (02) :269-322

[40]

Speicher R., 1998, COMBINATORIAL THEORY, V132

← 1 2 3 4 5 →