2020/09/09 by Michael de Moraes, de Moraes, Michael, Josnei Novacoski +1
Mathematics · #Meromorphic and Entire Functions #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2009.04349
The main goal of this paper is to characterize limit key polynomials for a valuation ν on K[x]. We consider the set Ψα of key polynomials for ν of degree α. We set p be the exponent characteristic of ν. Our first main result (Theorem 1.1) is that if Qα is a limit key polynomial for Ψα, then the degree of Qα is prα for some r∈\mathbb N. Moreover, in Theorem 1.2, we show that there exist Q∈Ψα and Qα a limit key polynomial for Ψα, such that the Q-expansion of Qα only has terms which are powers of p.