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arXiv · 1311.5909

On quadratic irrationals with bounded partial quotients

Jean Bourgain
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Abstract

It is shown that for some explicit constants $c>0, A>0$, the asymptotic for the number of positive non-square discriminants $D<x$ with fundamental solution $\varepsilon_D< x^{\frac 12+\alpha}, 0<\alpha <c$, remains preserved if we require moreover $\mathbb Q(\sqrt D)$ to contain an irrational with partial quotients bounded by $A$.

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Jean Bourgain. 2013-11-22. On quadratic irrationals with bounded partial quotients. https://arxiv.org/abs/1311.5909

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