Mahler series with multiplicative coefficient sequences
Number Theory
2026-03-25 v1
Abstract
We prove that every Mahler series, over a field of characteristic , with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit characterization of such series. This yields a joint extension of the characterization of rational series with multiplicative coefficients (by B\'ezivin and Bell--Bruin--Coons) and of multiplicative automatic sequences (by Konieczny--Lema\'nczyk--M\"ullner). Both of these results are used in our characterization, so we do not obtain new proofs of these special cases.
Cite
@article{arxiv.2603.23456,
title = {Mahler series with multiplicative coefficient sequences},
author = {Jason Bell and Daniel Smertnig},
journal= {arXiv preprint arXiv:2603.23456},
year = {2026}
}