On the length of rational continued fractions over $_q(X)$

S. Driss

ArticleOriginal scientific text

Title

On the length of rational continued fractions over $_q (X)$

Authors ¹

Affiliations

Faculté des Sciences de Sfax, Département de Mathématiques, BP 1171, Sfax 3000, Tunisie

Abstract

Let

_{q}

be a finite field and

A (Y) \in_{q} (X, Y)

. The aim of this paper is to prove that the length of the continued fraction expansion of

A (P); P \in_{q} [X]

, is bounded.

Keywords

ENG

continued fraction, formal power series, finite field

J.P. Allouche, Sur le développement en fraction continue de certaines séries formelles, C.R. Acad. Sciences 307 (1988), 631-633.
G. Grisel, Length of the Powers of a Rational Fraction, J. Number Theory 62 (1997), 322-337.
G. Choquet, Répartition des nombres $k {(\frac{3}{2})}^{n}$ et ensembles associés, (English summary) C.R. Acad. Sci. Paris Sér. A-B 290 13 (1980), 575-580.
M. Hbaib and M. Jellali, On the quadratic continued fractions over $F_{q} (X)$ , Communications in Algebra 38 (2010), 3181-3186.
A. Lasjaunias, Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic, J. Number Theory 65 (1997), 206-225.
M. Mendés France, Fractions continues limitées et théorie des languages, Séminaire Delange-Pisot-poitou. Théorie des nombres, 16 (1) (1971-1972), exp. no.9, 1-5.
M. Mendées France, Quelques problémes relatifs à la théorie des fractions continues limitées, Séminaire Delange-Pisot-poitou. Théorie des nombres 13 (1) (1971-1972), exp. no.2, 1-6.
M. Mendés France, Remarks and problems on finite and periodic continued fractions, Enseign. Math. 39 (1993), 249-257.
M. Mendés France, Sur les fractions continues limités, Acta Arith. 23 (1973), 207-215.
J. Mikusinski, Sur certaines fractions continues finies, Ann. Polon. Math. (1954), 203-206.
M. Mkaouar, Quelques propriétés métriques des fractions continues dans un corps fini, Soc. Math. Tunisie (1996), 120-130.
M. Mkaouar, Sur le développement en fraction continue des séries formelles quadratiques sur $F_{q} (X)$ , Acta Arith. XCII. 3 (2001), 241-251.

Title

On the length of rational continued fractions over _q(X)

Affiliations

Abstract

Keywords

Bibliography

On the length of rational continued fractions over $_q (X)$