ON THE VALUES OF SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR LIOUVILLE NUMBER ARGUMENTS

Abstract

In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or Sm i=1 Ui in Mahler’s classification of the complex numbers.