2025/11/09 by Coons, Michael, Mazáč, Jan, Pincus-Kazmar, Ari +1
Computer Science · Mathematics · #11B85 #37B10 #52C23 #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory
paper · doi:10.48550/arxiv.2511.06386
openalex publication_date 2025/11/09 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28
Recently, Baake and Coons proved several results on the average size of the autocorrelations of the Thue--Morse sequence. They also considered the absolute value of the autocorrelations, and showed that the average value of the autocorrelations is zero. In particular, they showed that ∑n\leqslant x|η(n)|=o(xα) for any α>log(3)/log(4). In this paper, we sharpen this result, providing upper and lower bounds for α. On the way to our lower bounds, we obtain the structure of the linear representation of the point-wise product of two k-regular sequences, which may be of independent interest.