English

Geodesic continued fractions and LLL

Number Theory 2018-04-12 v1

Abstract

We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to dd real numbers α1,,αd\alpha_1,\ldots,\alpha_d. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter tt as t0t\downarrow0. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in tt.

Keywords

Cite

@article{arxiv.1311.0455,
  title  = {Geodesic continued fractions and LLL},
  author = {Frits Beukers},
  journal= {arXiv preprint arXiv:1311.0455},
  year   = {2018}
}
R2 v1 2026-06-22T01:59:49.262Z