Werner Georg Nowak - On the critical determinants of certain star bodies

cm:9460 - Communications in Mathematics, June 28, 2017, Volume 25 (2017), Issue 1 - https://doi.org/10.1515/cm-2017-0002
On the critical determinants of certain star bodiesArticle

Authors: Werner Georg Nowak

    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.

    Volume: Volume 25 (2017), Issue 1
    Published on: June 28, 2017
    Imported on: May 11, 2022
    Keywords: General Mathematics,[MATH]Mathematics [math]

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