On some lacunary power series with algebraic coefficients and Mahler's U-numbers

Abstract

In this work, we consider some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m and show that under some conditions these series take values belonging to either the algebraic number field K or U(i-1)(m) U(i) in Mahler's classification of complex numbers for some Liouville number arguments. (C) 2011 Elsevier Inc. All rights reserved.