Distribution modulo one of linear recurrent sequences
Number Theory
2026-04-16 v1
Abstract
We study the distribution modulo one of linear recurrent sequences of real numbers. We prove criteria for the finiteness of the set of limit values of the fractional parts of such a sequence and give lower bounds for the maximal distance between two limit values. Our results generalize theorems of Flatto, Lagarias, Pollington, and Dubickas.
Cite
@article{arxiv.2604.14036,
title = {Distribution modulo one of linear recurrent sequences},
author = {Zhangchi Chen and Zihao Ye and Weizhe Zheng},
journal= {arXiv preprint arXiv:2604.14036},
year = {2026}
}
Comments
12 pages. This is an expanded version of Section 4 of arXiv:2511.21324v3