Correlation functions of the Rudin-Shapiro sequence

2022/11/02 by Jan Mazáč, Mazáč, Jan
Mathematics · #37B10 #52C23 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2211.01090

openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that all odd-point correlation functions of the balanced Rudin--Shapiro sequence vanish and that all even-point correlation functions depend only on a single number, which holds for any weighted correlation function as well. For the four-point correlation functions, we provide a more detailed exposition which reveals some arithmetic structures and symmetries. In particular, we show that one can obtain the autocorrelation coefficients of its topological factor with maximal pure point spectrum among them.

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