Year 2020, Volume 49 , Issue 1, Pages 45 - 55 2020-02-06

On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers

Gülcan KEKEÇ [1]


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.
Mahler’s classification of the transcendental numbers, Mahler’s S−number, Mahler’s T−number, Mahler’s U−number, Liouville number, power series
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0001-5805-7710
Author: Gülcan KEKEÇ
Institution: ISTANBUL UNIVERSITY
Country: Turkey


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms504560, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {45 - 55}, doi = {10.15672/HJMS.2018.650}, title = {On Mahler's \$S\$-numbers, \$T\$-numbers, and \$U\$-numbers}, key = {cite}, author = {KEKEÇ, Gülcan} }
APA KEKEÇ, G . (2020). On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 45-55 . DOI: 10.15672/HJMS.2018.650
MLA KEKEÇ, G . "On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 45-55 <https://dergipark.org.tr/en/pub/hujms/issue/52287/504560>
Chicago KEKEÇ, G . "On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 45-55
RIS TY - JOUR T1 - On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers AU - Gülcan KEKEÇ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/HJMS.2018.650 DO - 10.15672/HJMS.2018.650 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 45 EP - 55 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/HJMS.2018.650 UR - https://doi.org/10.15672/HJMS.2018.650 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers %A Gülcan KEKEÇ %T On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/HJMS.2018.650 %U 10.15672/HJMS.2018.650
ISNAD KEKEÇ, Gülcan . "On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 45-55 . https://doi.org/10.15672/HJMS.2018.650
AMA KEKEÇ G . On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 45-55.
Vancouver KEKEÇ G . On Mahler's $S$-numbers, $T$-numbers, and $U$-numbers. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 55-45.