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

S. Driss

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 2, page 131-137
  • ISSN: 1509-9415

Abstract

top
Let q be a finite field and A ( Y ) ∈ q ( X , Y ) . The aim of this paper is to prove that the length of the continued fraction expansion of A ( P ) ; P ∈ q [ X ] , is bounded.

How to cite

top

S. Driss. "On the length of rational continued fractions over $_q(X)$." Discussiones Mathematicae - General Algebra and Applications 35.2 (2015): 131-137. <http://eudml.org/doc/276460>.

@article{S2015,
abstract = {Let $_\{q\}$ be a finite field and $A(Y) ∈ _\{q\}(X,Y)$. The aim of this paper is to prove that the length of the continued fraction expansion of $A(P);P ∈ _\{q\}[X]$, is bounded.},
author = {S. Driss},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {continued fraction; formal power series; finite field},
language = {eng},
number = {2},
pages = {131-137},
title = {On the length of rational continued fractions over $_q(X)$},
url = {http://eudml.org/doc/276460},
volume = {35},
year = {2015},
}

TY - JOUR
AU - S. Driss
TI - On the length of rational continued fractions over $_q(X)$
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 2
SP - 131
EP - 137
AB - Let $_{q}$ be a finite field and $A(Y) ∈ _{q}(X,Y)$. The aim of this paper is to prove that the length of the continued fraction expansion of $A(P);P ∈ _{q}[X]$, is bounded.
LA - eng
KW - continued fraction; formal power series; finite field
UR - http://eudml.org/doc/276460
ER -

References

top
  1. [1] J.P. Allouche, Sur le développement en fraction continue de certaines séries formelles, C.R. Acad. Sciences 307 (1988), 631-633. Zbl0657.10035
  2. [2] G. Grisel, Length of the Powers of a Rational Fraction, J. Number Theory 62 (1997), 322-337. Zbl0878.11028
  3. [3] G. Choquet, Répartition des nombres k ( 3 / 2 ) n et ensembles associés, (English summary) C.R. Acad. Sci. Paris Sér. A-B 290 13 (1980), 575-580. Zbl0436.10025
  4. [4] M. Hbaib and M. Jellali, On the quadratic continued fractions over F q ( X ) , Communications in Algebra 38 (2010), 3181-3186. Zbl1219.11106
  5. [5] A. Lasjaunias, Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic, J. Number Theory 65 (1997), 206-225. Zbl0874.11051
  6. [6] 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. 
  7. [7] 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. 
  8. [8] M. Mendés France, Remarks and problems on finite and periodic continued fractions, Enseign. Math. 39 (1993), 249-257. Zbl0808.11007
  9. [9] M. Mendés France, Sur les fractions continues limités, Acta Arith. 23 (1973), 207-215. 
  10. [10] J. Mikusinski, Sur certaines fractions continues finies, Ann. Polon. Math. (1954), 203-206. Zbl0055.04501
  11. [11] M. Mkaouar, Quelques propriétés métriques des fractions continues dans un corps fini, Soc. Math. Tunisie (1996), 120-130. 
  12. [12] M. Mkaouar, Sur le développement en fraction continue des séries formelles quadratiques sur F q ( X ) , Acta Arith. XCII. 3 (2001), 241-251. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.