On the Distribution of Products of Primes and Powers
Number Theory
2015-06-10 v1
Abstract
We prove several results regarding the distribution of numbers that are the product of a prime and a -th power. First, we prove an asymptotic formula for the counting function of such numbers; this generalises a result of E. Cohen. We then show that the error term in this formula can be sharpened on the assumption of the Riemann hypothesis. Finally, we prove an asymptotic formula for these counting functions in short intervals.
Keywords
Cite
@article{arxiv.1506.02854,
title = {On the Distribution of Products of Primes and Powers},
author = {Adrian Dudek},
journal= {arXiv preprint arXiv:1506.02854},
year = {2015}
}
Comments
12 pages; feedback welcome