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

Maria Avdeeva; Dong Li; Yakov G. Sinai

doi:10.1007/s10955-013-0885-7

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

Maria Avdeeva
, Dong Li
, Yakov G. Sinai

Research output: Contribution to journal › Article › peer-review

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 Erdo{double acute}s-Kac type results.

Original language	English (US)
Pages (from-to)	327-333
Number of pages	7
Journal	Journal of Statistical Physics
Volume	154
Issue number	1-2
DOIs	https://doi.org/10.1007/s10955-013-0885-7
State	Published - Jan 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Erdo{double acute}s-Kac
Signed measure
Square-free

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10.1007/s10955-013-0885-7

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title = "New Erd{\H o}s-Kac Type Theorems for Signed Measures on Square-Free Integers",

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 Erdo\{double acute\}s-Kac type results.",

keywords = "Erdo\{double acute\}s-Kac, Signed measure, Square-free",

author = "Maria Avdeeva and Dong Li and Sinai, \{Yakov G.\}",

note = "Funding Information: 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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doi = "10.1007/s10955-013-0885-7",

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AU - Avdeeva, Maria

AU - Li, Dong

AU - Sinai, Yakov G.

N1 - Funding Information: 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.

PY - 2014/1

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N2 - 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 Erdo{double acute}s-Kac type results.

AB - 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 Erdo{double acute}s-Kac type results.

KW - Erdo{double acute}s-Kac

KW - Signed measure

KW - Square-free

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UR - https://www.scopus.com/pages/publications/84893798727#tab=citedBy

U2 - 10.1007/s10955-013-0885-7

DO - 10.1007/s10955-013-0885-7

M3 - Article

AN - SCOPUS:84893798727

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 1-2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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