Amou, Masaaki Approximation to certain transcendental decimal fractions by algebraic numbers. (English) Zbl 0718.11030 J. Number Theory 37, No. 2, 231-241 (1991). For a positive integer \(g\geq 2\) consider the number \(M(g)=0.(1)_ g(2)_ g...(n)_ g...\) where for \(n\in {\mathbb{N}}\) \((n)_ g\) means digit representation of n to base g and \(0.(1)_ g(2)_ g...\) means digit representation of the real M(g) to base g. It is known that M(g) is transcendental. The author gives estimates for Mahler’s function \(w_ d\) and for Koksma’s function \(w^*_ d\) of this number and he determines the exact value of the irrationality measure \(\mu (M(g)):=w_ 1(M(g))+1=w^*_ 1(M(g))+1\) of M(g), namely \(\mu M(g))=g\) for any \(g\geq 2\). Until now it was only known that \(\mu (M(g))\leq 2g^ 2/(g-1)\). Reviewer: G.Larcher (Salzburg) Cited in 2 ReviewsCited in 4 Documents MSC: 11J82 Measures of irrationality and of transcendence 11J17 Approximation by numbers from a fixed field 11A63 Radix representation; digital problems Keywords:decimal fractions; transcendence measure; digit representation; Mahler’s function; Koksma’s function; irrationality measure × Cite Format Result Cite Review PDF Full Text: DOI Online Encyclopedia of Integer Sequences: Decimal expansion of the binary Champernowne constant 0.862240125868... whose binary expansion is the concatenation of 1, 2, 3, ... written in binary. References: [1] Alladi, K.; Robinson, M. L., Legendre polynomials and irrationality, J. Reine angew. Math., 318, 135-155 (1980) · Zbl 0425.10039 [2] Danilov, L. V., Rational approximations of some functions at rational points, Math. Notes USSR, 24, 741-746 (1979) · Zbl 0418.10033 [3] Mahler, K., Arithmetische Eigenschaften einer Klasse von Dezimalbrüchen, Nederl. Akad. Wetensch. Proc. Ser. A., 40, 421-428 (1937) · JFM 63.0156.01 [4] Mahler, K., On a class of transcendental decimal fractions, Comm. Pure Appl. Math., 29, 717-725 (1976) · Zbl 0339.10025 [5] Schneider, Th., Einführung in die transzendenten Zahlen (1957), Springer-Verlag: Springer-Verlag Berlin · Zbl 0077.04703 [6] Shallit, J. O., Simple continued fractions for some irrational numbers, II, J. Number Theory, 14, 228-231 (1982) · Zbl 0481.10005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.