Finding simultaneous Diophantine approximations with prescribed quality

2010/01/25 by Wieb Bosma, Bosma, Wieb, Ionica Smeets +1 · 1 citation
Computer Science · Engineering · Mathematics · #11K60 #Advanced Numerical Analysis Techniques #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11K60

paper · pdf · doi:10.48550/arxiv.1001.4455

16 pages, 7 figures

arxiv created 2010/01/25 · openalex publication_date 2010/01/25 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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