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Padé approximations to solutions of linear differential equations and applications to diophantine analysis

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References

  1. A. Thue, J. Reine, Angew. Math. 135 (1909), 284–305.

    Google Scholar 

  2. C.L. Siegel, Math. Zeit. 10 (1921), 173–213.

    Article  Google Scholar 

  3. K.F. Roth., Mathematica 2 (1955), 1–20; corr. ibid., 168.

    Google Scholar 

  4. D. Ridout, Mathematica 4 (1957), 125–131.

    MathSciNet  Google Scholar 

  5. K. Mahler, Lectures on Diophantine Approximations, Notre Dame, 1961.

    Google Scholar 

  6. A. Ya. Khintchine, Continued fraction (translated by P. Wynn), P. Noordhoff, Gromingen, The Netherland, 1963.

    Google Scholar 

  7. S. Lang, Bull. Soc. Math. France 93 (1965), 177–192.

    MathSciNet  Google Scholar 

  8. S. Lang, Bull. Amer. Math. Soc. 77 (1971), 635–677.

    Article  MathSciNet  Google Scholar 

  9. D.V. Chudnovsky, G.V. Chudnovsky, see preceeding paper, this Volume.

    Google Scholar 

  10. S. Lang, Diophantine geometry, Interscience, N.Y., 1962.

    Google Scholar 

  11. S. Uchiyama, J. Faculty Sci. Hokkaido Univ. 15 (1961), 173–192.

    MathSciNet  Google Scholar 

  12. E.R. Kolchin, Proc. Amer. Math. Soc. 10 (1959), 238–244.

    Article  MathSciNet  Google Scholar 

  13. C.F. Osgood, Proc. Konink, Nederl. Akad. Van. Vetens (Amsterdam), Series A, 78 (1975), 105–119.

    MathSciNet  Google Scholar 

  14. C.F. Osgood, in Number Theory and Algebra, Academic Press, N.Y.-London, 1977, pp. 223–234.

    Google Scholar 

  15. C.F. Osgood, in Contribution to Algebra, Collection of papers dedicated to Ellis Kolchin, Academic Press, N.Y.-London, 1977, pp. 321–332.

    Google Scholar 

  16. W.M. Schmidt, Comm. Pure Appl. Math. 29 (1976), 759–773.

    Article  Google Scholar 

  17. W.M. Schmidt, Bull.Aust. Math. Soc. Ser. A, 25 (1978), 385–422.

    Article  Google Scholar 

  18. W.M. Schmidt, Montsh. Math. 87 (1979), 145–165.

    Article  Google Scholar 

  19. W.M. Schmidt, Diophantine approximations, Lectures Notes in Mathematics, v. 785, Springer Verlag, Berlin/N.Y., 1980.

    Google Scholar 

  20. C.F. Osgood, Notices of the Amer. Math. Soc. 1983, no. 4.

    Google Scholar 

  21. G.A. Baker, Jr., P. Graves-Morris, Padé approximants, Encycl. Math. v. 13, 14, ed. by G.-C. Rota, Addison Wesley, 1981.

    Google Scholar 

  22. A. Edrei, J. Approximation Theory 15 (1975), 278–293.

    Article  MathSciNet  Google Scholar 

  23. G.H. Halphen, Traité des fonctions elleptiques, Gauthier-Villars, Paris, 1888, v. II.

    Google Scholar 

  24. G. Frobenius, R. Stickelberger, J. Reine Angew, Math. 83 (1877), 179.

    MathSciNet  Google Scholar 

  25. S. Dumas, "Sur le développement des fonctions elliptiques en fractions continues", Thesis, Zurich, 1908.

    Google Scholar 

  26. E.M. Nikishin, Math. Sb. 143(1978), 280–292.

    Google Scholar 

  27. N.H. Abel, J. Reine Angew. Math. 1 (1826), 185–221 = Oeuvres, v. I, 104–144.

    Article  MathSciNet  Google Scholar 

  28. U. Toda, Theory of nonlinear lattices, Springer, N.Y. 1981.

    Book  MATH  Google Scholar 

  29. E.L. Ince, Ordinary differential equations, Chelsea, N.Y., 1956.

    MATH  Google Scholar 

  30. J. Nuttall, J. Approximation Theory 32 (1981), 233–240.

    Article  MathSciNet  Google Scholar 

  31. R.T. Baumel, J.L. Gammel, J. Nuttall, IMA Journal of Appl. Math. 27 (1981), 335–357.

    Article  MathSciNet  Google Scholar 

  32. E.R. Kolchin, Differential algebra and algebraic groups, Pure and Applied Mathematics, v. 54, Academic Press, N.Y./London, 1973.

    MATH  Google Scholar 

  33. M.F. Atiyah, I.G. Macdonald, Introduction to commutative algebra, Addison-Wesley, 1969.

    Google Scholar 

  34. G.V. Chudnovsky, Les Houches lectures, Lecture Notes Physics, v. 126, Springer, 1980, pp. 136–169.

    Google Scholar 

  35. R. Liouville, C.R. Acad. Sci. Paris, 89 (1879), 1108–1110.

    Google Scholar 

  36. A. Korkine, C.R. Acad. Sci. Paris, 90 (1880), 303–304.

    Google Scholar 

  37. V. Velmin, Math. Sb. 24 (1903–1904), 633–661.

    Google Scholar 

  38. L. Szpiro, Astérisque 86 (1981), 44–78.

    Google Scholar 

  39. Ju. I. Manin, Amer. Math. Soc. Translations (2) 50 (1966), 189–234.

    Article  MathSciNet  Google Scholar 

  40. P. Painlevé, Oeuvres, 3v., CNRS, Paris, 1972.

    Google Scholar 

  41. D.V. Chudnovsky, Cargése lectures, in Bifurcation phenomena in mathematical physics and related topics, D. Reidel, Boston, 1980, 385–447.

    Google Scholar 

  42. H. Davenport, Norske Vid. Selsk, Forh. 38 (1965), 86–87.

    MathSciNet  Google Scholar 

  43. M. Hall, in Computers in Number Theory, Academic Press, N.Y., 1971, 173–198.

    Google Scholar 

  44. C. L. Siegel, Abh. Preuss. Akad. Niss. no 1 (1929).

    Google Scholar 

  45. S. Lang, Mathematika 9 (1962), 157–161.

    Article  MathSciNet  Google Scholar 

  46. A. Galoćkin, Math. Sb. 95 (1974), 396–417.

    Google Scholar 

  47. K. Weierstrass, S.-B.K. Preuss. Akad. Wiss. Berlin (1885), 1067–1085.

    Google Scholar 

  48. K. Mahler, J. Reine Angew. Math. 166 (1932), 118–136.

    MathSciNet  Google Scholar 

  49. G.V. Chudnovsky, Ann. Math. 109 (1979), 353–376.

    Article  MathSciNet  Google Scholar 

  50. G.V. Chudnovsky, Ann. Math. 117 (1983), 325–382.

    Article  MathSciNet  Google Scholar 

  51. G.V. Chudnovsky, Proc. Natl. Acad. Sci. USA 80 (1983), 3138–3141.

    Article  MathSciNet  Google Scholar 

  52. A. Baker, Transcendental number theory, 2nd edition, Cambridge Univ. Press, 1979.

    Google Scholar 

  53. B.J. Birch, in Computers in Algebra and Number Theory, Proc. Symp. Appl. Math., v. 4, AMS, Providence, Rhode Island, 1971, 63–68.

    Google Scholar 

  54. B. Riemann, Oeuvres Mathematiques, Blanchard, Paris, 1968, 353–363.

    Google Scholar 

  55. G.V. Chudnovsky, Cargése lectures, in Bifurcation phenomena in mathematical physics and related topics, D. Reidel, Boston, 1980, 448–510.

    Google Scholar 

  56. G. Pólya, G. Szegö, Aufgaben and lehrsätze aus der analysis, Springer, N.Y., 1964, v. II.

    Book  MATH  Google Scholar 

  57. A. Baker, Proc. Camb. Phil. Soc. 63 (1967), 693–702.

    Article  Google Scholar 

  58. N. Ratliff, J. Number Theory 10 (1978), 99–126.

    Article  MathSciNet  Google Scholar 

  59. K. Vaananen, Acta Arith. 36 (1980), 273–295.

    MathSciNet  Google Scholar 

  60. W.W. Adams, Proc. Natl. Acad. Sci. USA 55 (1966), 28–31.

    Article  Google Scholar 

  61. W.M. Schmidt, Equations over finite fields, Lecture Notes Math., v. 536, Springer, N.Y. 1976.

    MATH  Google Scholar 

  62. F. Sakai, Invent. Math. 26 (1974), 212–229.

    Article  Google Scholar 

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David V. Chudnovsky Gregory V. Chudnovsky Harvey Cohn Melvin B. Nathanson

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© 1984 Springer-Verlag

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Chudnovsky, D.V., Chudnovsky, G.V. (1984). Padé approximations to solutions of linear differential equations and applications to diophantine analysis. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071541

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  • DOI: https://doi.org/10.1007/BFb0071541

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