2024/04/14 by Chunlin Wang, Wang, Chunlin
Mathematics · #11B85 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2404.09175
openalex publication_date 2024/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that any power series over a finite field represents a rational function if and only if its sequence of coefficients is ultimately periodic. The famous Christol's Theorem states that a power series over a finite field is algebraic if and only if its sequence of coefficients is p-automatic. In this paper, we extend these two results to expansions of elements in the completion of a global function field under a nontrivial valuation. As application of our generalization of Christol's theorem, we answer some questions about β-expansions of formal Laurent series over finite fields.