Real Mahler Series

Abstract

Let $\alpha$ and $\beta$ be positive real numbers. Let $F(x)\in K[[x^{\Gamma }]]$ be a Hahn series. We prove that if $F(x)$ is both $\alpha$-Mahler and $\beta$-Mahler then it must be a rational function, $F(x)\in K(x)$, assuming some non-degeneracy conditions on $\alpha$ and $\beta$.

19 pages