Finding simultaneous Diophantine approximations with prescribed quality

Details Finding simultaneous Diophantine approximations with prescribed quality Finding simultaneous Diophantine approximations with prescribed quality

2010-01-25

arxiv.org/abs/1001.4455v1

Mathematics

Number Theory

16 pages, 7 figures

Scientific paper

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 the LLL-algorithm for lattice basis reduction. We present a
version of the algorithm that runs in polynomial time of the input.

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