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...
Saved in:
Published in | Taiwanese journal of mathematics Vol. 18; no. 1; pp. 1 - 26 |
---|---|
Main Author | |
Format | Journal Article |
Language | English |
Published |
Mathematical Society of the Republic of China
01.02.2014
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |