On Mahler's Classification of Formal Power Series Over a Finite Field-Reference-Cited by-同舟云学术

On Mahler's Classification of Formal Power Series Over a Finite Field

Published:2022-02-01 Issue:1 Volume:72 Page:265-273
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Kekeç Gülcan¹

Affiliation:

1. Department of Mathematics , Faculty of Science, Istanbul University , 34134 Vezneciler, Fatih , Istanbul , TURKEY

Abstract

Abstract Let K be a finite field, K(x) be the field of rational functions in x over K and

be the field of formal power series over K. We show that under certain conditions integral combinations with algebraic formal power series coefficients of a U 1-number in

are Um -numbers in

, where m is the degree of the algebraic extension of K(x), determined by these algebraic formal power series coefficients.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2022-0017/pdf

Reference17 articles.

1. ALNIAҪIK, K.: On the subclasses Umin Mahler’s classification of the transcendental numbers, İstanbul Üniv. Fen Fak. Mecm. Ser. A 44(1979), 39–82.

2. BUGEAUD, Y.: Approximation by Algebraic Numbers, Cambridge Tracts in Math. 160, Cambridge University Press, Cambridge, 2004.

3. BUNDSCHUH, P.: Transzendenzmasse in Körpern formaler Laurentreihen, J. Reine Angew. Math. 299/300(1978), 411–432.

4. CHAVES, A. P.—MARQUES, D.: An explicit family of Um-numbers, Elem. Math. 69(2014), 18–22.

5. CHAVES, A. P.—MARQUES, D.—TROJOVSKÝ, P.: On the arithmetic behavior of Liouville numbers under rational maps, Bull. Braz. Math. Soc. New Series 52(2021), 803—813.

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