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Paul Mercat
Construction de fractions continues périodiques uniformément bornées
(Construction of periodic continuous fractions uni- formly bounded)
Journal de théorie des nombres de Bordeaux, 25 no. 1 (2013), p. 111-146, doi: 10.5802/jtnb.829
Article PDF | Reviews MR 3063834 | Zbl 1272.11019

Résumé - Abstract

We build, for real quadratic fields, infinitely many periodic continuous fractions uniformly bounded, with a seemingly better bound than the known ones. We do that using continuous fraction expansions with the same shape as those of real numbers $\sqrt{n} + n$. It allows us to obtain that there exist infinitely many quadratic fields containing infinitely many continuous fraction expansions formed only by integers $1$ and $2$. We also prove that a conjecture of Zaremba implies a conjecture of McMullen, building periodic continuous fractions from continous fraction expansions of rational numbers.

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