Some Lacunary Power Series and Mahler’s Um-numbers in p-adic Domain

Abstract

In this paper, we consider some lacunar power series in Q_p, where p is a prime number. We obtain some results about lacunary power series with rational coefficients for U_m-number arguments in Q_p. We determined whether the values of the considered lacunar power series belong to a certain field of algebraic numbers or to the set of transcendental numbers in Q_p. Also, we find similar results for lacunary power series with p-adic algebraic coefficients.