2010/01/18 by Alina Firicel, Firicel, Alina
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1001.3127
arxiv created 2010/01/18 · openalex publication_date 2010/01/18 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1976, Baum and Sweet gave the first example of a power series that is algebraic over the field \mathbb F2(T) and whose continued fraction expansion has partial quotients with bounded degree. This power series is the unique solution of the equation TX3+X-T=0. In 1986, Mills and Robbins described an algorithm that allows to compute the continued fraction expansion of the Baum--Sweet power series. In this paper, we consider the more general equations TXr+1+X-T=0, where r is a power of a prime number p. Such an equation has a unique solution in the field \mathbb Fp((T-1)). Applying an approach already used by Lasjaunias, we give a description of the continued fraction expansion of these algebraic power series.