Lengths of periods of continued fractions of square roots of integers. (English) Zbl 1208.11013
Empirical study of the period length \(T\) of the continued fractions of \(\sqrt{Q}\) (for growing integers \(Q\)) shows several strange asymptotic results, for instance, \(T\leq C \sqrt{Q}\ln Q\). These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.
Reviewer: Oleg Karpenkov (Graz)
Keywords:
Gauss-Kuzmin theorem; odd period lengths of continued fractions; statistics of continued fractionsReferences:
| [1] | Arnold VI (2008) Statistics of the periods of continued fractions for quadratic irrationals. Izv Math 72(1):1–34 · Zbl 1152.11002 · doi:10.1070/IM2008v072n01ABEH002389 |
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