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Effective bounds on the diophantine approximation of algebraic functions, and nevanlinna theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1052)

Keywords

  • Characteristic Zero
  • Algebraic Number
  • Diophantine Equation
  • Algebraic Function
  • Algebraic Differential Equation

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References

  1. Roth, K.F. Rational approximation to algebraic numbers. Mathematika 2, 1–20 (with corrigendum p. 168), (1955).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Liouville, J. C.R. Acad. Sci. (Paris) 18, 883–885, 910–911. Also J. Math pures appl. (1) 16, 133–142 (1851).

    Google Scholar 

  3. Feldman, N.I. An effective refinement of the exponent in Liouville's Theorem, Izv. Akad. Nauk SSSR, Ser. mat. 35, 973–990. Math USSR Izv. 5, 985–1002 (1972).

    Google Scholar 

  4. Uchiyama, S. Rational approximations to algebraic functions, J. Fac. Sci. Hokkaido Univ., Ser. 15, (1961) 173–192.

    MathSciNet  MATH  Google Scholar 

  5. Maillet, E., Introduction a la theorie des nombres transcendants et des proprietes arithmetiques des fonctiones, Paris, 1906.

    Google Scholar 

  6. Osgood, C.F., Effective Bounds on the "Diophantine Approximation" of Algebraic Functions over Fields of Arbitrary Characteristic and Applications to Differential Equations, Proc. Koninkl. Nederl. Akademie Van Wetenschappen, Series A, 78 No. 2 (1975), 105–119 (errata 78, No. 5).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Mathematical Developments Arising from Hilbert Problems, Proceedings of Symposia in Pure Mathematics, Vol. XXVIII, A.M.S. Providence, Rhode Island, 1976.

    Google Scholar 

  8. Kolchin, E.R., Rational approximations to solutions of algebraic differential equations, Proc. Amer. Math. Soc. 10 (1959), 238–244.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Osgood, C.F. An effective lower bound on the "diophantine" approximation of algebraic functions by rational functions (II), Contributions to Algebra: a collection of papers dedicated to Ellis Kolchin 321–327, Academic Press, 1977.

    Google Scholar 

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© 1984 Springer-Verlag

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Osgood, C.F. (1984). Effective bounds on the diophantine approximation of algebraic functions, and nevanlinna theory. 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/BFb0071547

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  • DOI: https://doi.org/10.1007/BFb0071547

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12909-7

  • Online ISBN: 978-3-540-38788-6

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