On continued fractions and diophantine approximation in power series fields

• Autorzy: Wolfgang M. Schmidt
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 95
• Numer: 2
• Strony: 139-166

Daty

wydano

2000

otrzymano

1998-11-09

Twórcy

autor

Wolfgang M. Schmidt

• 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.