On Mahler’s S-numbers, T-numbers, and U-numbers

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:1
On Mahler’s S-numbers, T-numbers, and U-numbers

On Mahler’s S-numbers, T-numbers, and U-numbers

Pages : 45-55

View : 62 | Download : 7

Publication Date : 2020-02-06

Article Type : Research Paper

Abstract :In this work, we consider some power series with algebraic coefficients from a certain algebraic number field, whose radiuses of convergence are infinite. We show that under certain conditions these series take transcendental values at non-zero algebraic number arguments, and we determine the classes to which these transcendental values belong in Mahler`s classification. Then we consider these series for certain Liouville number arguments and obtain similar results.
Keywords : Mahlers classification of the transcendental numbers, Mahlers S number, Mahlers T number, Mahlers U number, Liouville number, power series

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