- 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(xα), 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.
- 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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