Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

Abstract

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.