CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Author's Draft

The Rudin-Shapiro sequence and similar sequences are normal along squares

  • Clemens Müllner,
    Institut für Diskrete Mathematik und Geometrie TU Wien, Wiedner Hauptstr. 8-10, 1040 Wien, Austria
Format:   LaTeX   MathJax   PDF  

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
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/