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On the residue class distribution of the number of prime divisors of an integer

Published online by Cambridge University Press:  11 January 2016

Michael Coons  and
Sander R. Dahmen
Michael Coons
Affiliation:
University of Waterloo, Department of Pure Mathematics, Waterloo, Ontario, N2L 3G1, Canada, mcoons@math.uwaterloo.ca
Sander R. Dahmen
Affiliation:
Mathematisch Instituut, Universiteit Utrecht, P.O. Box 80 010, 3508 TA Utrecht, The Netherlandss.r.dahmen@uu.nl
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Abstract

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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,…,m – 1, we have

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

Keywords

11N3711N6011N2511M41
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 202 , June 2011 , pp. 15 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

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