On the complexity of algebraic numbers, II. Continued fractions

@article{Adamczewski2005OnTC,
title={On the complexity of algebraic numbers, II. Continued fractions},
journal={Acta Mathematica},
year={2005},
volume={195},
pages={1-20}
}
• Published 2005
• Mathematics
• Acta Mathematica
The continued fraction expansion of an irrational number $\alpha$ is eventually periodic if and only if $\alpha$ is a quadratic irrationality. However, very little is known regarding the size of the partial quotients of algebraic real numbers of degree at least three. Because of some numerical evidence and a belief that these numbers behave like most numbers in this respect, it is often conjectured that their partial quotients form an unbounded sequence. More modestly, we may expect that if the… Expand
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