The Rudin–Shapiro Sequence and Similar Sequences Are Normal Along Squares

DOI10.4153/CJM-2017-053-1zbMath1446.11012arXiv1704.06472OpenAlexW2963084560MaRDI QIDQ4561107

Clemens Müllner

Publication date: 10 December 2018

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06472

zbMATH Keywords

normalityexponential sumdigital sequenceRudin-Shapiro sequence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Radix representation; digital problems (11A63) Trigonometric and exponential sums (general theory) (11L03) Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. (11K16) Automata sequences (11B85) Distribution functions associated with additive and positive multiplicative functions (11N60)

Related Items (10)

How to prove that a sequence is not automatic ⋮ On the maximum order complexity of Thue-Morse and Rudin-Shapiro sequences along polynomial values ⋮ Normality of the Thue-Morse function for finite fields along polynomial values ⋮ Pseudorandom sequences derived from automatic sequences ⋮ Discrete correlations of order 2 of generalised Rudin-Shapiro sequences: a combinatorial approach ⋮ Möbius orthogonality of sequences with maximal entropy ⋮ On the \(N\)th maximum order complexity and the expansion complexity of a Rudin-Shapiro-like sequence ⋮ On the distribution of the Rudin-Shapiro function for finite fields ⋮ Gowers norms for the Thue-Morse and Rudin-Shapiro sequences ⋮ (Logarithmic) densities for automatic sequences along primes and squares

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