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June 2011 On the residue class distribution of the number of prime divisors of an integer
Michael Coons, Sander R. Dahmen
Nagoya Math. J. 202: 15-22 (June 2011). DOI: 10.1215/00277630-1260423

Abstract

Let Ω(n) denote the number of prime divisors of n counting multiplicity. One can show that for any positive integer m and all j=0,1,,m1, we have

#{nx:Ω(n)j(modm)}=xm+o(xα),

with α=1. Building on work of Kubota and Yoshida, we show that for m>2 and any j=0,1,,m1, the error term is not o(xα) for any α<1.

Citation

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Michael Coons. Sander R. Dahmen. "On the residue class distribution of the number of prime divisors of an integer." Nagoya Math. J. 202 15 - 22, June 2011. https://doi.org/10.1215/00277630-1260423

Information

Published: June 2011
First available in Project Euclid: 31 May 2011

zbMATH: 1257.11087
MathSciNet: MR2804543
Digital Object Identifier: 10.1215/00277630-1260423

Subjects:
Primary: 11N37, 11N60
Secondary: 11M41, 11N25

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.202 • June 2011
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