A density version of Cobham's theorem
Number Theory
2017-11-02 v2 Formal Languages and Automata Theory
Combinatorics
Abstract
Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version of the result: if two sequences which are automatic with respect to two multiplicatively independent bases coincide on a set of density one, then they also coincide on a set of density one with a periodic sequence. We apply the result to a problem of Deshouillers and Ruzsa concerning the least nonzero digit of in base .
Cite
@article{arxiv.1710.07261,
title = {A density version of Cobham's theorem},
author = {Jakub Byszewski and Jakub Konieczny},
journal= {arXiv preprint arXiv:1710.07261},
year = {2017}
}
Comments
10 pages