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arXiv · 1311.0455

Geodesic continued fractions and LLL

Frits Beukers
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Abstract

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

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Frits Beukers. 2013-11-03. Geodesic continued fractions and LLL. https://arxiv.org/abs/1311.0455

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