Taiwanese Journal of Mathematics

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

Gülcan Kekeç

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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.

Article information

Source
Taiwanese J. Math., Volume 18, Number 1 (2014), 1-26.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706328

Digital Object Identifier
doi:10.11650/tjm.18.2014.2285

Mathematical Reviews number (MathSciNet)
MR3162110

Zentralblatt MATH identifier
1357.11064

Subjects
Primary: 11J82: Measures of irrationality and of transcendence 11J61: Approximation in non-Archimedean valuations

Keywords
Mahler's classification of the complex numbers and of the $p-$adic numbers Mahler's $U-$number Mahler's $p-$adic $U-$number lacunary power series transcendence measure

Citation

Kekeç, Gülcan. SOME GENERALIZED LACUNARY POWER SERIES WITH ALGEBRAIC COEFFICIENTS FOR MAHLER'S $U-$NUMBER ARGUMENTS. Taiwanese J. Math. 18 (2014), no. 1, 1--26. doi:10.11650/tjm.18.2014.2285. https://projecteuclid.org/euclid.twjm/1499706328


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