On Mahler’sS-numbers,T-numbers, andU-numbers

Abstract

In this work, we consider some power series with algebraic coefficients from a certainalgebraic number field, whose radiuses of convergence are infinite. We show that undercertain conditions these series take transcendental values at non-zero algebraic numberarguments, and we determine the classes to which these transcendental values belongin Mahler’s classification. Then we consider these series for certain Liouville numberarguments and obtain similar results.