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

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

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

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