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The Rudin-Shapiro Sequence and Similar Sequences are Normal Along Squares

  Published:2018-04-30
 Printed: Oct 2018
  • Clemens Müllner,
    Institut für Diskrete Mathematik und Geometrie TU Wien, Wiedner Hauptstr. 8-10, 1040 Wien, Austria
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Abstract

We prove that digital sequences modulo $m$ along squares are normal, which covers some prominent sequences like the sum of digits in base $q$ modulo $m$, the Rudin-Shapiro sequence and some generalizations. This gives, for any base, a class of explicit normal numbers that can be efficiently generated.
Keywords: Rudin-Shapiro sequence, digital sequence, normality, exponential sum Rudin-Shapiro sequence, digital sequence, normality, exponential sum
MSC Classifications: 11A63, 11B85, 11L03, 11N60, 60F05 show english descriptions Radix representation; digital problems {For metric results, see 11K16}
Automata sequences
Trigonometric and exponential sums, general
Distribution functions associated with additive and positive multiplicative functions
Central limit and other weak theorems
11A63 - Radix representation; digital problems {For metric results, see 11K16}
11B85 - Automata sequences
11L03 - Trigonometric and exponential sums, general
11N60 - Distribution functions associated with additive and positive multiplicative functions
60F05 - Central limit and other weak theorems
 

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