A Transcendental Unbounded Continued Fraction Expansions over A Finite Field

Rima Ghorbel; Hassen Kthiri

doi:10.22342/jims.27.1.829.115-122

Rima Ghorbel ⁽¹⁾ , Hassen Kthiri ⁽²⁾

(1) ,

(2) University of Sfax

https://doi.org/10.22342/jims.27.1.829.115-122

Issue
VOLUME 27 NUMBER 1 (MARCH 2021)

Submitted
May 11, 2019

Accepted
February 26, 2021

Published
March 31, 2021

Keywords:

Continued fraction, formal power series, transcendence, finite fields.

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Abstract

Let Fq be a finite field and Fq((X−1 )) the field of formal power series with coefficients in Fq. The purpose of this paper is to exhibit a family of transcendental continued fractions of formal power series over a finite field through some specific irregularities of its partial quotients

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Authors

Rima Ghorbel

Hassen Kthiri

University of Sfax

hassenkthiri@gmail.com (Primary Contact)

Ghorbel, R., & Kthiri, H. (2021). A Transcendental Unbounded Continued Fraction Expansions over A Finite Field. Journal of the Indonesian Mathematical Society, 27(1), 115–122. https://doi.org/10.22342/jims.27.1.829.115-122