By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequenc...

In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler’s Um−number arguments belong to either a certain algebraic number field or ⋃t i=1 Ui 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. Mo...