Correlation of the Rudin-Shapiro sequence along prime numbers

Autor:	Popoli, Pierre
Rok vydání:	2023
Předmět:	Mathematics - Number Theory 11A07 11A41 11A63 11B85 11K45 11L07 11L20
Druh dokumentu:	Working Paper
Popis:	The correlation measure of order $k$ is a measure of pseudorandomness that quantifies the similarity between a sequence and its shifts. It is known that the correlation of order 4 is large for the Rudin-Shapiro sequence despite having nice pseudorandom properties with respect to the correlation of order 2. In this paper, we prove a radically different behavior along the subsequence of prime numbers and continue the investigation towards the pseudorandomness of subsequences of automatic sequences. This result generalizes the result of Aloui, Mauduit, and Mkaouar (2021) about the correlation of the sum of digits function along prime numbers. Comment: 19 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.10629 Zobrazit plný text záznamu View this record from Arxiv