On the critical determinants of certain star bodies - Archive ouverte HAL
Article Dans Une Revue Communications in Mathematics Année : 2017

On the critical determinants of certain star bodies

Werner Georg Nowak
  • Fonction : Auteur correspondant

Résumé

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.
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hal-03664940 , version 1 (11-05-2022)

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Werner Georg Nowak. On the critical determinants of certain star bodies. Communications in Mathematics, 2017, Volume 25 (2017), Issue 1 (1), pp.5 - 11. ⟨10.1515/cm-2017-0002⟩. ⟨hal-03664940⟩
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