2013/03/08 by Boris Adamczewski, Adamczewski, Boris, Jason P. Bell +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.CO #math.NT #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1303.2019
52 pages
arxiv created 2013/03/08 · openalex publication_date 2013/03/08 · arxiv updated 2013/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a field of characteristic zero and k and l be two multiplicatively independent positive integers. We prove the following result that was conjectured by Loxton and van der Poorten during the Eighties: a power series F(z)∈ K[[z]] satisfies both a k- and a l-Mahler type functional equation if and only if it is a rational function.