Best Simultaneous Diophantine Approximations under a Constraint on the Denominator

Details Best Simultaneous Diophantine Approximations under a Constraint on the Denominator Best Simultaneous Diophantine Approximations under a Constraint on the Denominator

2005-10-08

arxiv.org/abs/math/0510164v2

Mathematics

Number Theory

17 pages, corrected typos

Scientific paper

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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