PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2000 | 95 | 2 | 139-166
Tytuł artykułu

On continued fractions and diophantine approximation in power series fields

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
95
Numer
2
Strony
139-166
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-11-09
Twórcy
  • Department of Mathematics, University of Colorado, Boulder, CO 80309-0395, U.S.A.
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav95z2p139bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.