Continuous Distribution Arising From the Three Gaps Theorem
Number Theory
2015-12-01 v1
Abstract
The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts . It is known that if one averages over {\alpha}, the distribution becomes continuous. We present an alternative approach, which establishes this averaged result and also provides good bounds for the error terms.
Cite
@article{arxiv.1511.09399,
title = {Continuous Distribution Arising From the Three Gaps Theorem},
author = {Geremías Polanco and Daniel Schultz and Alexandru Zaharescu},
journal= {arXiv preprint arXiv:1511.09399},
year = {2015}
}
Comments
23 pages including references, Four figures