On Pisot's d-th root conjecture for function fields and related GCD estimates
Abstract
We propose a function-field analog of Pisot's d-th root conjecture on linear recurrences, and prove it under some “non-triviality” assumption. Besides a recent result of Pasten-Wang on Büchi's d-th power problem, our main tool, which is also developed in this paper, is a function-field analog of a GCD estimate in a recent work of Levin and Levin-Wang. As an easy corollary of such a GCD estimate, we also obtain an asymptotic...
Paper Details
Title
On Pisot's d-th root conjecture for function fields and related GCD estimates
Published Date
Feb 1, 2022
Journal
Volume
231
Pages
401 - 432
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