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 $\bigcup_{i=1}^{t} U_{i}$ 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 $\mathbb{Q}_{p}$ of $p-$adic numbers.
Citation
Gülcan Kekeç. "SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR MAHLER'S $U-$NUMBER ARGUMENTS." Taiwanese J. Math. 18 (1) 1 - 26, 2014. https://doi.org/10.11650/tjm.18.2014.2285
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