Shallit, Jeffrey Real numbers with bounded partial quotients: A survey. (English) Zbl 0753.11006 Enseign. Math., II. Sér. 38, No. 1-2, 151-187 (1992). In a regular continued fraction expansion \(x=[a_ 0,a_ 1,a_ 2,\ldots]\) of real numbers \(x\), where \(a_ 0\) is integer and \(a_ j\), \(j\geq 1\), are positive integers, the partial quotients \(a_ j\) are unbounded for almost all \(x\) with respect to Lebesgue measure. In fact, an accurate formula is available on the growth of the maximum of \(a_ 1,a_ 2,\ldots,a_ n\) valid for almost all \(x\) [see J. Galambos, Acta Arith. 25, 359-364 (1974; Zbl 0255.60033)]. Yet, continued fractions with bounded \(a_ j\) play an important role in a variety of fields. The author surveys such applications. Reviewer: J.Galambos (Philadelphia) Cited in 1 ReviewCited in 30 Documents MSC: 11A55 Continued fractions 11K50 Metric theory of continued fractions 11-02 Research exposition (monographs, survey articles) pertaining to number theory Keywords:bounded partial quotient; number of constant type; algebraic numbers; metric theory; discrepancy; survey of applications; regular continued fraction Citations:Zbl 0255.60036; Zbl 0255.60033 PDFBibTeX XMLCite \textit{J. Shallit}, Enseign. Math. (2) 38, No. 1--2, 151--187 (1992; Zbl 0753.11006)