Distribution modulo one of linear recurrent sequences
Zhangchi Chen, Zihao Ye, and Weizhe Zheng
TL;DR
This paper investigates the distribution properties of linear recurrent sequences modulo one, establishing criteria for the finiteness of their fractional limit values and providing bounds on their maximal gaps.
Contribution
It generalizes existing theorems by offering new criteria and bounds for the distribution of fractional parts of linear recurrent sequences.
Findings
Criteria for finiteness of limit fractional parts set
Lower bounds for maximal distance between limit values
Generalization of previous theorems by Flatto, Lagarias, Pollington, and Dubickas
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.
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