SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR MAHLER'SU–NUMBER ARGUMENTS

In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler'sUm –number arguments belong to either a certain algebraic number field or ∪ i = 1 t U i in Mahler's classification of the complex numbers, wheret...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 18; no. 1; pp. 1 - 26
Main Author Kekeç, Gülcan
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2014
Subjects
Algebra
Coefficients
Complex numbers
Integers
Mathematical theorems
Polynomials
Power series
Power series coefficients
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Summary:In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler'sUm –number arguments belong to either a certain algebraic number field or ∪ i = 1 t U i in Mahler's classification of the complex numbers, wheretdenotes 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 ofp–adic numbers. 2010Mathematics Subject Classification: 11J82, 11J61. Key words and phrases: Mahler's classification of the complex numbers and of thep–adic numbers, Mahler'sU–number, Mahler'sp–adicU–number, Lacunary power series, Transcendence measure.
ISSN:1027-5487
2224-6851