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Successive Minima and Best Simultaneous Diophantine Approximations

Iskander Aliev·Martin Henk
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Abstract

We study the problem of best approximations of a vector $α\in{\mathbb R}^n$ by rational vectors of a lattice $Λ\subset {\mathbb R}^n$ whose common denominator is bounded. To this end we introduce successive minima for a periodic lattice structure and extend some classical results from geometry of numbers to this structure. This leads to bounds for the best approximation problem which generalize and improve former results.

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Iskander Aliev, Martin Henk. 2005-03-17. Successive Minima and Best Simultaneous Diophantine Approximations. https://arxiv.org/abs/math/0503365

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