Residue races of the number of prime divisors function

Abstract

We investigate the distribution of the function $\omega (n)$, the number of distinct prime divisors of $n$, in residue classes modulo $q$ for natural numbers $q$ greater than 2. In particular we ask `prime number races' style questions, as suggested by Coons and Dahmen in their paper `On the residue class distribution of the number of prime divisors of an integer'.

10 pages, 2 figures