The virtual periods of linear recurrence sequences in cyclotomic fields
Number Theory
2021-10-05 v3
Abstract
A linear recurrence sequence in a cyclotomic field produces a sequence of the generating fields of each term. We show that the later sequence is periodic after removing the first finite terms, and give a bound of its period. This can be applied to exponential sums.
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Cite
@article{arxiv.2010.08342,
title = {The virtual periods of linear recurrence sequences in cyclotomic fields},
author = {Shenxing Zhang},
journal= {arXiv preprint arXiv:2010.08342},
year = {2021}
}
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5 pages