Vol. 1, No. 1, 2013

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Finding simultaneous Diophantine approximations with prescribed quality

Wieb Bosma and Ionica Smeets

Vol. 1 (2013), No. 1, 167–185
Abstract

We give an algorithm that finds a sequence of approximations with Dirichlet coefficients bounded by a constant only depending on the dimension. The algorithm uses LLL lattice basis reduction. We present a version of the algorithm that runs in polynomial time of the input.

Keywords
simultaneous Diophantine approximation, LLL lattice reduction
Mathematical Subject Classification 2010
Primary: 11J13
Secondary: 11Y16, 11J70
Milestones
Published: 14 November 2013
Authors
Wieb Bosma
Mathematics Department
Radboud University Nijmegen
PO Box 9010
6500 Nijmegen
The Netherlands
Ionica Smeets
Mathematical Institute
Leiden University
Niels Bohrweg 1
2333 CA Leiden
The Netherlands