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

Title: On the residue class distribution of the number of prime divisors of an integer
Creator: Coons, Michael; Dahmen, Sandler R.
Relation: Nagoya Mathematical Journal Vol. 202, Issue June 2011, p. 15-22
Publisher Link: http://dx.doi.org/10.1215/00277630-1260423
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2011
Description: 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 #{n ≤ x : Ω(n) ≡ j(modm} = x/m + o(x^α), 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(x^α) for any α < 1.
Subject: residue class; prime divisors; Liouville function; Riemann zeta function; prime number theory
Identifier: http://hdl.handle.net/1959.13/1354756
Identifier: uon:31341
Identifier: ISSN:0027-7630
Language: eng
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