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Successive Minima and Best Simultaneous Diophantine Approximations

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Abstract.

We study the problem of best approximations of a vector \(\alpha\in{\Bbb R}^n\) by rational vectors of a lattice \(\Lambda\subset{\Bbb R}^n\) 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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Authors and Affiliations

  1. University of Edinburgh, United Kingdom

    Iskander Aliev

  2. Universität Magdeburg, Germany

    Martin Henk

Authors
  1. Iskander Aliev
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  2. Martin Henk
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Aliev, I., Henk, M. Successive Minima and Best Simultaneous Diophantine Approximations. Mh Math 147, 95–101 (2006). https://doi.org/10.1007/s00605-005-0344-x

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  • DOI: https://doi.org/10.1007/s00605-005-0344-x

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