Algebraic Degree Periodicity in Recurrence Sequences
Number Theory
2020-10-01 v1
Abstract
The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal polynomial sequence for exponential sums over finite fields. The degree periodicity also holds for some more complicated non-linear recurrence sequences. We give one example from the iterations of a polynomial map. This depending on the dynamic Mordell-Lang conjecture which has been proved in some cases.
Cite
@article{arxiv.2009.14382,
title = {Algebraic Degree Periodicity in Recurrence Sequences},
author = {Daqing Wan and Hang Yin},
journal= {arXiv preprint arXiv:2009.14382},
year = {2020}
}