Successive Minima and Best Simultaneous Diophantine Approximations |
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Authors: | Iskander Aliev Martin Henk |
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Institution: | University of Edinburgh, United Kingdom Universit?t Magdeburg, Germany
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Abstract: | We study the problem of best approximations of a vector
by rational vectors of a lattice
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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Keywords: | 2000 Mathematics Subject Classification: 11J13 11H06 11H31 52C07 |
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