Diophantine approximation with smooth numbers
Number Theory
2020-09-14 v2
Abstract
We prove a theorem about approximation to an irrational number by rational numbers whose denominator n is free of prime factors bigger than a power of log n. We strengthen the result in version 1 by using an exponential sum over smooth numbers tailored to the application. The new exponent approaches 1/3 as the exponent of log n becomes large.
Cite
@article{arxiv.2007.05823,
title = {Diophantine approximation with smooth numbers},
author = {Roger Baker},
journal= {arXiv preprint arXiv:2007.05823},
year = {2020}
}