Download PDF - On continued fractions and diophantine approximation in power series fieldsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On continued fractions and diophantine approximation in power series fields

Authors 1

Affiliations

  1. Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, U.S.A.

Bibliography

  1. N. H. Abel, Über die Integration der Differential-Formel ρdx/√R wenn R und ρ ganze Funktionen sind, J. Reine Angew. Math. 1 (1826), 185-221.
  2. L. E. Baum and M. M. Sweet, Continued fractions of algebraic power series in characteristic 2, Ann. of Math. 103 (1976), 593-610.
  3. L. E. Baum and M. M. Sweet, Badly approximable power series in characteristic 2, ibid. 105 (1977), 573-580.
  4. M. W. Buck and D. P. Robbins, The continued fraction expansion of an algebraic power series satisfying a quartic equation, J. Number Theory 50 (1995), 335-344.
  5. J. H. Davenport, On the Integration of Algebraic Functions, Lecture Notes in Comput. Sci. 102, Springer, 1981.
  6. G. H. Halphen, Traité des fonctions elliptiques et de leurs applications, Vol. II, Paris, 1891.
  7. Y. Hellegouarch et M. Lozach, Équation de Pell et points d'ordre fini, avec 'Appendice' de M. Lozach, manuscript, Caen, 1981.
  8. A. Lasjaunias, Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic, J. Number Theory 65 (1997), 206-225.
  9. A. Lasjaunias, Continued fractions for algebraic power series over a finite field, Finite Fields Appl. 5 (1999), 46-56.
  10. A. Lasjaunias and B. de Mathan, Thue's Theorem in positive characteristic, J. Reine Angew. Math. 473 (1996), 195-206.
  11. A. Lasjaunias and B. de Mathan, Differential equations and diophantine approximation in positive characteristic, Monatsh. Math. 473 (1996), 195-206.
  12. B. de Mathan, Approximations diophantiennes dans un corps local, Bull. Soc. Math. France, Suppl. Mém. 21 (1970).
  13. B. de Mathan, Approximation exponents of algebraic functions in positive characteristic, Acta Arith. 60 (1992), 359-370.
  14. B. Mazur, Rational points on modular curves, in: Modular Functions of One Variable, V (Bonn, 1976), Lecture Notes in Math. 601, Springer, 1977, 107-148.
  15. L. Merel, Bornes pour la torsion des courbes elliptiques sur les corps de nombres, Invent. Math. 124 (1996), 437-449.
  16. W. H. Mills and D. P. Robbins, Continued fractions for certain algebraic power series, J. Number Theory 23 (1986), 388-404.
  17. T. Nagell, Problems in the theory of exceptional points on plane cubics of genus one, Den 11te Skandinaviske Matematikerkongress, Trondheim, 1949, 71-76.
  18. C. F. Osgood, Effective bounds on the 'diophantine approximation' of algebraic functions over fields of arbitrary characteristic and applications to differential equations, Indag. Math. 37 (1975), 105-119.
  19. O. Perron, Die Lehre von den Kettenbrüchen, Vol. I, 3rd ed., Teubner, Stuttgart, 1954.
  20. A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith. 6 (1961), 393-413.
  21. A. Schinzel, On some problems of the arithmetical theory of continued fractions II, ibid. 7 (1962), 287-298. Corrigendum, ibid. 47 (1987), 295.
  22. J. A. Serret, Handbuch der höheren Algebra, Vol. I (German translation of French original), 1878.
  23. P. Tchebycheff, Sur l'intégration des différentielles qui contiennent une racine carrée d'un polynome du troisième ou du quatrième degré, J. Math. Pures Appl. (2) 9 (1864), 225-246.
  24. J. F. Voloch, Diophantine approximation in positive characteristic, Period. Math. Hungar. 19 (1988), 217-225.
  25. J. F. Voloch, Diophantine approximation in characteristic p, Monatsh. Math. 119 (1995), 321-325.
Acta Arithmetica
2000/95/2
Export to PBN, Opens in new tab
Pages:
139-166
Main language of publication
English
Received
1998-11-09
Published
2000
Exact and natural sciences