Journal of Statistical Physics

, Volume 154, Issue 1–2, pp 327–333 | Cite as

New Erdős-Kac Type Theorems for Signed Measures on Square-Free Integers

Article

Abstract

We consider a family of signed measures supported on the set of square-free numbers. We prove some local limit theorems for the prime divisor counting function ω(n) and establish new Erdős-Kac type results.

Keywords

Erdős-Kac Square-free Signed measure 

Notes

Acknowledgements

D. Li was supported in part by NSF under agreement No. DMS-1128155. Ya.G. Sinai was supported by the NSF grant No. DMS-0901235. D. Li was also supported by an Nserc Discovery grant.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Landau Institute of Theoretical PhysicsMoscowRussia

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