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On Benford’s law for continued fractions. (English) Zbl 0728.11036
A sequence of real numbers \((q_ n)\) is said to obey Benford’s law, if the decimal logarithms (lg \(q_ n)\) are uniformly distributed modulo 1. H. Jager and P. Liardet [Indagationes Math. 50, 181-197 (1988; Zbl 0655.10045)] have proved Benford’s law for the sequence of denominators \(q_ n(\omega)\) of the continued fraction expansion of a quadratic irrational \(\omega\). In the present article this statement is generalized to regular Hurwitz continued fractions. Furthermore Benford’s law is obtained for almost all real numbers \(\omega\).
Reviewer: R.F.Tichy (Graz)
MSC:
11K06 General theory of distribution modulo \(1\)
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
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