English

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 kkth powers inside arbitrary arithmetic progressions whose step has O(1)O(1) many divisors.

Keywords

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

R2 v1 2026-06-23T06:24:31.784Z