Continued 𝜷-fractions with Pisot unit base in 𝑭𝒒 ((𝒙−𝟏)) Continued 𝜷-fractions with Pisot unit base in 𝑭𝒒 ((𝒙−𝟏))

Main Article Content

Rania Kammoun

Abstract

In this paper, we are interested in introducing a new theory of continued fractions based on the beta-expansion theory in the field of Laurent series over a finite field 𝐹𝑞. We will characterize all elements having finite continued beta-fraction where the base is a unit Pisot quadratic series.
Classification Mathematic Subject: 11R06, 37B50.

Article Details

Section
Research Article