Year: 2022
Type: preprint
Abstract: Given an integer linear recurrence sequence $\langle X_n \rangle_n$, the Skolem Problem asks to determine whether there is a natural number $n$ such that $X_n = 0$. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.
Source: arXiv (Cornell University)
Author: Kenison, George
Institution: TU Wien
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226491538