Best Simultaneous Diophantine Approximations under a Constraint on the Denominator
Number Theory
2007-05-23 v2
Abstract
We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximation constants are given in terms of critical determinants of suitable star bodies. Tools are results on simultaneous Diophantine approximation of rationals by rationals with smaller denominator. Finally, the approximation results are applied to the decomposition of integer vectors.
Cite
@article{arxiv.math/0510164,
title = {Best Simultaneous Diophantine Approximations under a Constraint on the Denominator},
author = {Iskander Aliev and Peter Gruber},
journal= {arXiv preprint arXiv:math/0510164},
year = {2007}
}
Comments
17 pages, corrected typos