PUB - Publikationen an der Universität Bielefeld

The pair correlations of the Thue-Morse sequence and system are revisited, with focus on asymptotic results on various means. First, it is shown that all higher-order correlations of the Thue-Morse sequence with general real weights are effectively determined by a single value of the balanced 2-point correlation. As a consequence, we show that all odd-order correlations of the balanced Thue-Morse sequence vanish, and that, for any even n , the n-point correlations of the balanced Thue-Morse sequence have mean value zero, as do their absolute values, raised to an arbitrary positive power. All these results also apply to the entire Thue-Morse system. We finish by showing how the correlations of the Thue-Morse system with general real weights can be derived from the balanced 2-point correlations. (c) 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.