Sharp bounds for symmetric and asymmetric Diophantine approximation
Number Theory
2009-08-25 v2
Abstract
In 2004, J.C. Tong found bounds for the approximation quality of a regular continued fraction convergent of a rational number, expressed in bounds for both the previous and next approximation. We sharpen his results with a geometric method and give both sharp upper and lower bounds. We also calculate the asymptotic frequency that these bounds occur.
Cite
@article{arxiv.0806.1457,
title = {Sharp bounds for symmetric and asymmetric Diophantine approximation},
author = {Cor Kraaikamp and Ionica Smeets},
journal= {arXiv preprint arXiv:0806.1457},
year = {2009}
}
Comments
16 pages, 5 figures