Article Sidebar

Submitted
June 13, 2017
Accepted
April 10, 2018
Published
July 10, 2019
Download
PDF
Statistic
Read Counter : 758 Download : 314

Downloads

Download data is not yet available.

Main Article Content

Abstract

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.

Article Details

How to Cite
Driss, S., & Kthiri, H. (2019). On The Geometric Continued Fractions in Positive Characteristic. Journal of the Indonesian Mathematical Society, 25(2), 139–145. https://doi.org/10.22342/jims.25.2.525.139-145
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. bibitem{AB} B. Adamczewski and Y. Bugea., “On the Maillet-Baker continued fractions”, {em J. Reine Angew. Math.},
  2. textbf{606} (2007), 105-121.
  3. bibitem{B} A. Baker. , “Continued fractions of trascendental numbers”, {em Mathematika.}, textbf{9} (1962), 1-8.
  4. bibitem{ABOS} A. Baker., “On Mahler's classification of transcendental numbers”, {em Acta Math.}, textbf{111} (1964), 97–120.
  5. bibitem{BS} L.E. Baum and H.M. Sweet., “Continued fractions of algebraic power series in characteristic 2”,{em Ann. Math.},
  6. textbf{103} (1976), 593-610.
  7. bibitem{jlddac} J. L. Davison., “A class of transcendental numbers with bounded partial quotients”, {em In
  8. In R. A. Mollin, ed., Number Theory and Applications}, pp. 365–371, Kluwer Academic
  9. Publishers, 1989.
  10. bibitem{hdkf} H. Davenport., K.F. Roth., “Rational approximations to algebraic numbers”,
  11. {em Mathematika.}, textbf{2} (1955) 160–167.
  12. bibitem{HMT} M. Hbaib, M. Mkaouar and K. Tounsi., “Un crit`{e}re de transcendance dans le corps des s'eries
  13. formelles $mathbb{F}_q((X^{-1}))$”, {em J. Number Theory.}, textbf{116} (2006), 140-149.
  14. bibitem{K} A. Khintchine., “Continued fractions”,
  15. {em Gosudarstv.} Izdat. Tech-Teor. Lit. Moscow-Leningrad, 2$^{nd}$ edition, 1949, (In Russian).
  16. bibitem{L} J. Liouville., “Sur des classes tr`{e}s 'etendues de quantit'es dont la valeur n'est ni alg'ebrique ni m^eme r'eductibles `{a} des rationnelles alg'ebriques”, {em J. Math. Pures Appl.}, textbf{16} (1851), 133-142.
  17. bibitem{M} E. Maillet., “Introduction `{a} la th'eorie des nombres transcendants et des propri'et'es arithm'etiques des fonctions”,
  18. {em Gauthier-Villars.}, Paris, 1906.
  19. bibitem{MR} W.H. Mills and D.P. Robbins., “Continued fractions for certain algebraic power series”,
  20. {em J. Number Theory.}, textbf{23} (1986), 388-404.
  21. bibitem{M1} M. Mkaouar., “Fractions continues et s'eries formelles alg'ebriques r'eduites”,
  22. {em Port. Math.}, textbf{58} (2001).
  23. bibitem{M2} M. Mkaouar., “Transcendance de certaines fractions continues dans le corps des s'eries formelles”,
  24. {em J. Algebra.}, textbf{281} (2004), 502-507.
  25. bibitem{P} O. Perron., “Die Lehre von den Kettenbr"{u}chen”, {em Teubner}, Leipzig, 1929.
  26. bibitem{sh} W.M. Schmidt., “Diophantine approximation”, {em Lecture Notes in Mathematics}, vol. 785. Springer, Berlin (1980)