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α-expansions, linear recurrences, and the sum-of-digits function

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Abstract

We give a generalization of the ordinaryq-ary digit expansion of positive integers to arbitrary real bases α>1. We investigate the properties of the sum-of-digit functions(n). We give an asymptotic formula for the sum ∑ n<N s(itn) and consider the distribution properties of the sequencexs(n) for irrationalx.

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Authors and Affiliations

  1. Institut für Analysis, Technische Mathematik und Versicherungsmathematik, TU Wien, Wiedner Hauptstraße 8-10, A-1040, Wien, Austria

    Peter J. Grabner

  2. Institut für Mathematik, TU Graz, Steyrergasse 30, A-8010, Graz, Austria

    Robert F. Tichy

Authors
  1. Peter J. Grabner
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  2. Robert F. Tichy
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This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990.

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Grabner, P.J., Tichy, R.F. α-expansions, linear recurrences, and the sum-of-digits function. Manuscripta Math 70, 311–324 (1991). https://doi.org/10.1007/BF02568381

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  • DOI: https://doi.org/10.1007/BF02568381

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