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On the denominators in Sylvester’s series. (English) Zbl 0587.10028

Suitably normalized, the logarithms of the denominators of a Sylvester series form a convergent sequence. The nature of the limit function, and the convergence to it, are discussed. The limit function is believed to be the first explicitly defined function known to have jointly continuous occupation density.

MSC:

11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
26A30 Singular functions, Cantor functions, functions with other special properties
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