On the length of the period of a quadratic irrationality

The estimate
$$ Q(D)\asymp\sqrt DL_{4D}(1),\qquad D\to\infty, $$
is proved, where $Q(D)$ is the number of reduced binary quadratic forms of discriminant $4D$ and $L_{4D}(s)=\sum^\infty_{n=1}\bigl(\frac{4D}n\bigr)n^{-s}$ is a Dirichlet $L$-series.
Results concerning individual estimates of $l/\log\varepsilon$ are also obtained, where $l$ is the length of the period of the continued-fraction expansion of $\xi\in\mathbf Q(\sqrt D)$ and $\varepsilon$ is a fundamental unit of the field $\mathbf Q(\sqrt D)$.
Bibliography: 12 titles.