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.
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Research supported in part by NSF Grants DMS 1301619.
