Residue races of the number of prime divisors function

Sam Porritt

Residue races of the number of prime divisors function

Number Theory 2018-06-06 v1

Authors: Sam Porritt

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'.

Keywords

number of prime divisors residue classes prime number races arithmetic functions distribution modulo q

Cite

@article{arxiv.1806.01585,
  title  = {Residue races of the number of prime divisors function},
  author = {Sam Porritt},
  journal= {arXiv preprint arXiv:1806.01585},
  year   = {2018}
}

Comments

10 pages, 2 figures

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