Affiliation:
1. Institute of Mathematics, Department of Integrative Biology, BOKU Wien, 1180 Vienna , Austria
Abstract
Abstract
In a classic paper [14], W.G. Spohn established the to-date sharpest estimates from below for the simultaneous Diophantine approximation constants for three and more real numbers. As a by-result of his method which used Blichfeldt’s Theorem and the calculus of variations, he derived a bound for the critical determinant of the star body
|x1|(|x1|3 + |x2|3 + |x3|3 ≤ 1.
In this little note, after a brief exposition of the basics of the geometry of numbers and its significance for Diophantine approximation, this latter result is improved and extended to the star body
|x1|(|x1|3 + |x2
2 + x3
2)3/2≤ 1.
Reference14 articles.
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