M\"obius orthogonality for $q$-semimultiplicative sequences
Number Theory
2018-08-21 v1 Combinatorics
Dynamical Systems
Abstract
We show that all -semimultiplicative sequences are asymptotically orthogonal to the M\"obius function, thus proving the Sarnak conjecture for this class of sequences. This generalises analogous results for the sum-of-digits function and other digital sequences which follow from previous work of Mauduit and Rivat.
Cite
@article{arxiv.1808.06196,
title = {M\"obius orthogonality for $q$-semimultiplicative sequences},
author = {Jakub Konieczny},
journal= {arXiv preprint arXiv:1808.06196},
year = {2018}
}
Comments
19 pages