## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 25, Number 5 (2018), 777-792.

### On the multiplication by a polynomial of bounded continued fraction over a finite field

Khalil Ayadi, Awatef Azaza, and Iheb Elouaer

#### Abstract

In this paper, we will discuss the period length of the continued fraction of the product of a polynomial with a quadratic power series over a finite field. Furthermore, we will give the first example of bounded continued fraction in characteristic 3 with not flat partial quotients.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 5 (2018), 777-792.

**Dates**

First available in Project Euclid: 18 January 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1547780435

**Digital Object Identifier**

doi:10.36045/bbms/1547780435

**Mathematical Reviews number (MathSciNet)**

MR3901846

**Zentralblatt MATH identifier**

07038552

**Subjects**

Primary: 11J70: Continued fractions and generalizations [See also 11A55, 11K50] 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15]

**Keywords**

finite fields formal power series continued fraction

#### Citation

Ayadi, Khalil; Azaza, Awatef; Elouaer, Iheb. On the multiplication by a polynomial of bounded continued fraction over a finite field. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 777--792. doi:10.36045/bbms/1547780435. https://projecteuclid.org/euclid.bbms/1547780435