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Frequencies of digits under trigonometric perturbations

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Abstract

We study the Hausdorff dimension of a class of sets of real numbers defined in terms of frequencies of digits in some integer base m, with the frequencies related by trigonometric perturbations. We show in particular that the Hausdorff dimension is analytic in the parameter determining the perturbation, and we obtain estimates for the coefficients of the corresponding power series in terms of m. We also compute the first terms of the series.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisbon, Portugal

    Luis Barreira & Claudia Valls

Authors
  1. Luis Barreira
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  2. Claudia Valls
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Corresponding author

Correspondence to Luis Barreira.

Additional information

Communicated by K. Schmidt.

Partially supported by FCT through CAMGSD, Lisbon. L. Barreira was also supported by the FCT grant SFRH/BSAB/960/2009.

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Barreira, L., Valls, C. Frequencies of digits under trigonometric perturbations. Monatsh Math 167, 357–374 (2012). https://doi.org/10.1007/s00605-012-0389-6

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  • DOI: https://doi.org/10.1007/s00605-012-0389-6

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