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arXiv · 1601.08109

Construction of uniformly bounded periodic continued fractions

Paul Mercat
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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 continued fraction expansions of rational numbers.

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Paul Mercat. 2016-01-29. Construction of uniformly bounded periodic continued fractions. https://arxiv.org/abs/1601.08109

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