On the number of $k$th powers inside arithmetic progressions
Number Theory
2018-12-11 v2 Classical Analysis and ODEs
Abstract
We find upper bounds that are sharp for the number of th powers inside arbitrary arithmetic progressions whose step has many divisors.
Cite
@article{arxiv.1811.11919,
title = {On the number of $k$th powers inside arithmetic progressions},
author = {Jean Bourgain and Ciprian Demeter},
journal= {arXiv preprint arXiv:1811.11919},
year = {2018}
}
Comments
This version presents a much simpler argument and works for all powers