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Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

Asymptotic free probability for arithmetic functions and factorization of Dirichlet series 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 $$GL_n$$ G L n . We then study conditions under which a Dirichlet series may be factored into a product of automorphic L-functions using asymptotic freeness. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Asymptotic free probability for arithmetic functions and factorization of Dirichlet series

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-015-0117-1
Publisher site
See Article on Publisher Site

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

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 3, 2015

References