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Spring 1999 Congruence properties of the $\Omega$-function on sumsets
J. Rivat, A. Sárközy, C. L. Stewart
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Illinois J. Math. 43(1): 1-18 (Spring 1999). DOI: 10.1215/ijm/1255985334


In this article we investigate the behaviour of the omega function, which counts the number of prime factors of an integer with multiplicity, as one runs over those integers of the form $a + b$ where $a$ is from a set $A$ and $b$ is from a set $B$. We prove, for example, that if $A$ and $B$ are sufficiently dense subsets of the first $N$ positive integers and $k$ is a positive integer then the number of pairs $(a,b)$ for which the omega function of $a + b$ lies in a given residue class modulo $k$ is roughly the total number of pairs divided by $k$.


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J. Rivat. A. Sárközy. C. L. Stewart. "Congruence properties of the $\Omega$-function on sumsets." Illinois J. Math. 43 (1) 1 - 18, Spring 1999.


Published: Spring 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0926.11075
MathSciNet: MR1665708
Digital Object Identifier: 10.1215/ijm/1255985334

Primary: 11N64
Secondary: 11N36

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 1 • Spring 1999
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