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An infinite sequence with finitely many distinct letters is said to have the uniform distribution property if all letters in the alphabet of the sequence have the same density in all arithmetical progressions. This property was first studied by Gelfond for sum of digits functions. In this note, we characterize a larger class of purely automatic sequences with the same property.

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Purely Automatic Sequences with the Uniform Distribution Property

  • 会议论文

  • 发表日期：

    2025年

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  • Shuo Li,
  • Narad Rampersad

摘要

An infinite sequence with finitely many distinct letters is said to have the uniform distribution property if all letters in the alphabet of the sequence have the same density in all arithmetical progressions. This property was first studied by Gelfond for sum of digits functions. In this note, we characterize a larger class of purely automatic sequences with the same property.