On quadratic irrationals with bounded partial quotients

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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 \(\varepsilon _D<x^{\frac{1}{2}+\alpha }\), \(0<\alpha <c\), remains preserved if we require moreover \(\mathbb Q(\sqrt{D})\) to contain an irrational with partial quotients bounded by A.

Mathematics Subject Classification

11D09 11L05 

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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