SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR MAHLER'S U - NUMBER ARGUMENTS

Abstract

In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler's U-m-number arguments belong to either a certain algebraic number field or U-i=1 U-i in Mahler's classification of the complex numbers, where t denotes a positive rational integer dependent on the coefficients of the given series and on the argument. Moreover, the obtained results are adapted to the field Q(p) of p-adic numbers.