On Pisot's $d$-th root conjecture for function fields and related GCD estimates
Number Theory
2020-10-06 v1
Abstract
We propose a function-field analog of Pisot's -th root conjecture on linear recurrences, and prove it under some "non-triviality" assumption. Besides a recent result of Pasten-Wang on B{\"u}chi's -th power problem, our main tool, which is also developed in this paper, is a function-field analog of an GCD estimate in a recent work of Levin and Levin-Wang. As an easy corollary of such GCD estimate, we also obtain an asymptotic result.
Cite
@article{arxiv.2010.01896,
title = {On Pisot's $d$-th root conjecture for function fields and related GCD estimates},
author = {Ji Guo and Chia-Liang Sun and Julie Tzu-Yueh Wang},
journal= {arXiv preprint arXiv:2010.01896},
year = {2020}
}