English

M\"obius orthogonality for $q$-semimultiplicative sequences

Number Theory 2018-08-21 v1 Combinatorics Dynamical Systems

Abstract

We show that all qq-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

R2 v1 2026-06-23T03:37:42.807Z