Best Simultaneous Diophantine Approximations under a Constraint on the Denominator

2005/10/08 by Iskander Aliev, Aliev, Iskander, Peter M. Gruber +1
Computer Science · Mathematics · Physics and Astronomy · #11H06 #11J13 #52C07 #Advanced Mathematical Theories and Applications #Chaos-based Image/Signal Encryption #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.math/0510164

openalex publication_date 2005/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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