On Mahler’s p-adic S-, T -, and U-numbers-Reference-Cited by-同舟云学术

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

Published:2020-03-01 Issue:1 Volume:28 Page:81-94
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Bugeaud Yann¹,Kekeç Gülcan²

Affiliation:

1. Université de Strasbourg, CNRS , IRMA UMR 7501, 7, rue René Descartes, 67000 Strasbourg , France .

2. Istanbul University , Faculty of Science, Department of Mathematics , 34134, Vezneciler- Istanbul , Turkey .

Abstract

Abstract We consider some lacunary power series with rational coefficients in 𝕈p. We show that under certain conditions these series take transcendental values at non-zero rational number arguments, and we determine the classes of these transcendental values with respect to Mahler’s classification of p-adic numbers.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2020-0005

Reference13 articles.

1. [1] B. Adamczewski, Y. Bugeaud, Mesures de transcendance et aspects quantitatifs de la méthode de Thue-Siegel-Roth-Schmidt, Proc. London Math. Soc.101 (2010), 1-26.10.1112/plms/pdp054

2. [2] A. Baker, On Mahler’s classification of transcendental numbers, Acta Math.111 (1964), 97-120.10.1007/BF02391010

3. [3] Y. Bugeaud, Approximation by Algebraic Numbers, Cambridge Tracts in Mathematics, 160 (Cambridge University Press, Cambridge, 2004).10.1017/CBO9780511542886

4. [4] Y. Bugeaud, G. Kekeç, On Mahler’s classification of p-adic numbers, Bull. Aust. Math. Soc.98 (2018), 203-211.10.1017/S0004972718000515

5. [5] K. Mahler, Zur Approximation der Exponentialfunktionen und des Logarithmus. I, II, J. reine angew. Math.166 (1932), 118-150.10.1515/crll.1932.166.137

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Transcendental Regular Continued Fractions;Mathematica Slovaca;2023-12-01