Successive Minima and Best Simultaneous Diophantine Approximations

2005/03/17 by Iskander Aliev, Aliev, Iskander, Martin Henk +1
Mathematics · #11H06 #11H31 #11J13 #52C07 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11H06 #msc:11H31 #msc:11J13 #msc:52C07

paper · pdf · doi:10.48550/arxiv.math/0503365

8 pages

arxiv created 2005/03/17 · arxiv updated 2009/12/01

Abstract

We study the problem of best approximations of a vector α∈\mathbb Rⁿ by rational vectors of a lattice Λ⊂ \mathbb Rⁿ 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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