Arithmetical properties of the values of power series (Analytic Number Theory and Related Areas)

Abstract

In this paper, we give a new criterion for the algebraic independence of the values of power series. In particular, we deduce the algebraic independence of the values displaystyle sum_{m=0}^{infty}$beta$^{-w_{m}}, where $beta$ is a Pisot or Salem number and (w_{m})_{rn=0}^{infty} is a certain increasing sequence of nonnegative integers satisfying mathrm{h}mathrm{m}_{mrightarrowinfty}w_{m+1}/w_{m}=1.