Best simultaneous diophantine approximations under a constraint on the denominator

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 and Gruber, Peter M. 2006. Best simultaneous diophantine approximations under a constraint on the denominator. Contributions to Discrete Mathematics 1 (1) , pp. 29-46.

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
ISSN:	1715-0868
Last Modified:	13 Jan 2023 02:14
URI:	https://orca.cardiff.ac.uk/id/eprint/70675

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