Successive Minima and Best Simultaneous Diophantine Approximations

Details Successive Minima and Best Simultaneous Diophantine Approximations Successive Minima and Best Simultaneous Diophantine Approximations

2005-03-17

arxiv.org/abs/math/0503365v1

Mathematics

Number Theory

8 pages

Scientific paper

We study the problem of best approximations of a vector $\alpha\in{\mathbb R}^n$ by rational vectors of a lattice $\Lambda\subset {\mathbb R}^n$ 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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