A NOTE ON CONTINUED FRACTIONS WITH SEQUENCES OF PARTIAL QUOTIENTS OVER THE FIELD OF FORMAL POWER SERIES

2012 ◽  
Vol 49 (4) ◽  
pp. 875-883
Author(s):  
Xuehai Hu ◽  
Luming Shen
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Continued Fractions ◽  
Partial Quotients ◽  
Formal Power

scholarly journals A Transcendental Unbounded Continued Fraction Expansions over A Finite Field

2021 ◽  
Vol 27 (1) ◽  
pp. 115-122
Author(s):  
Rima Ghorbel ◽  
Hassen Kthiri
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Partial Quotients ◽  
Continued Fraction Expansions ◽  
Formal Power

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

scholarly journals A transcendence criterion for continued fraction expansions in positive characteristic

2015 ◽  
Vol 98 (112) ◽  
pp. 237-242
Author(s):  
Basma Ammous ◽  
Sana Driss ◽  
Mohamed Hbaib
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Positive Characteristic ◽  
Partial Quotients ◽  
Continued Fraction Expansions ◽  
Formal Power

We exhibit a family of transcendental continued fractions of formal power series over a finite field through some specific irregularities of its partial quotients.

ON TRANSCENDENTAL CONTINUED FRACTIONS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

2021 ◽  
pp. 1-12
Author(s):  
BÜŞRA CAN ◽  
GÜLCAN KEKEÇ
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Finite Fields ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Continued Fraction Expansions ◽  
Formal Power

Abstract In the field of formal power series over a finite field, we prove a result which enables us to construct explicit examples of $U_{m}$ -numbers by using continued fraction expansions of algebraic formal power series of degree $m>1$ .

Continued fractions for quadratic elements in formal power series

2011 ◽  
Vol 26 (3) ◽  
pp. 399-405
Author(s):  
Jun-Ichi Tamura ◽  
Shin-Ichi Yasutomi
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Continued Fractions ◽  
Formal Power

scholarly journals On The Geometric Continued Fractions in Positive Characteristic

2019 ◽  
Vol 25 (2) ◽  
pp. 139-145
Author(s):  
Sana Driss ◽  
Hassen Kthiri
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Positive Characteristic ◽  
Formal Power

In this paper we study another form in the field of formal power series over a finite field. If the continued fraction of a formal power seriesin $\mathbb{F}_q((X^{-1}))$ begins with sufficiently largegeometric blocks, then $f$ is transcendental.

Sign in / Sign up

Export Citation Format

Share Document