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A generalization of Sándor’s theorem using iterated logarithms. (English) Zbl 1220.11087

The authors prove a theorem dealing with linear independence of special infinite series. The terms of this series consist of rational numbers and converge very rapidly to zero. Their proof uses ideas from the work of J. Sándor [Stud. Univ. Babes-Bolyai, Math. 29, 3–12 (1984; Zbl 0544.10033)] and the work of the first author and S. Sobková [Tsukuba J. Math. 27, No. 2, 341–357 (2003; Zbl 1057.11035)].

MSC:

11J72 Irrationality; linear independence over a field
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