Best simultaneous diophantine approximations of some cubic algebraic numbers

Nicolas Chevallier

Displaying similar documents to “Best simultaneous diophantine approximations of some cubic algebraic numbers”

On a mixed problem in Diophantine approximation

Yann Bugeaud, Bernard de Mathan (2009)

Acta Arithmetica

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Simultaneous Diophantine approximation and asymptotic formulae on manifolds

Glyn Harman (2003)

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On the critical determinants of certain star bodies

Werner Georg Nowak (2017)

Communications in Mathematics

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In a classic paper, 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 $| x_{1} | ({| x_{1} |}^{3} + {| x_{2} |}^{3} + {| x_{3} |}^{3}) \leq 1 .$ 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...