Pisot numbers, Salem numbers, and generalised polynomials
Number Theory
2023-02-14 v1 Combinatorics
Dynamical Systems
Abstract
We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type. To this end, we introduce the notion of a generalised polynomial on a number field. We establish a connection between the existence of generalised polynomial expressions for sets of values of linear recurrent sequences and for subsemigroups of multiplicative groups of number fields.
Cite
@article{arxiv.2302.06242,
title = {Pisot numbers, Salem numbers, and generalised polynomials},
author = {Jakub Byszewski and Jakub Konieczny},
journal= {arXiv preprint arXiv:2302.06242},
year = {2023}
}
Comments
18 pages