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Pade-approximations in number theory

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Padé Approximation and its Applications Amsterdam 1980

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 888))

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References

  • [A-R] K. Alladi, M. Robinson, On certain irrational values of the logarithm, Lecture Notes in Math. 751, 1–9.

    Google Scholar 

  • [A] R. Apéry, Irrationalité de ζ(2) et ζ(3) “Journées arithmétiques de Luminy”, Astérisque no 61, 1979, 11–13.

    MATH  Google Scholar 

  • [Ba1] A. Baker, Rational approximations to \(^3 \surd 2\) and other algebraic numbers, Quart. J. Math. Oxford, 15(1964), 375–383.

    Article  MathSciNet  MATH  Google Scholar 

  • [Ba2] A. Baker, Transcendental Number Theory (Cambridge, 1975).

    Google Scholar 

  • [Be1] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc., 11(1979), 268–272.

    Article  MathSciNet  MATH  Google Scholar 

  • [Be2] F. Beukers, Legendre polynomials in irrationality proofs, Bull. Australian Math. Soc. (to appear).

    Google Scholar 

  • [Be3] F. Beukers, The generalised Ramanujan-Nagell equation, Thesis, University of Leiden (1979), also to appear in Acta Arithmetica.

    Google Scholar 

  • [C1] G.V. Chudnovsky, C.R. Acad. Sc. Paris, 288(1979), 607–609, 965–967, 1001–1003.

    MathSciNet  Google Scholar 

  • [C2] G.V. Chudnovsky, Padé-approximations to the generalized hypergeometric functions I, J. Math. pures et appl. 58(1979), 445–476.

    MathSciNet  MATH  Google Scholar 

  • [C3] G.V. Chudnovsky, Rational and Padé-approximations to solutions of linear differential equations and the monodromy theory, Lecture Notes in Physics 126, 136–169.

    Google Scholar 

  • [C4] G.V. Chudnovsky, Padé-approximation and the Riemann monodromy problem, Proceedings of the NATO Advanced Study Institute, held at Cargèse, Corsica, France, June 24–July 7, 1979.

    Google Scholar 

  • [D] Y. DOMAR, On the diophantine equation |Axn−Byn|=1, n≥5, Math. Scand. 2(1954), 29–32.

    MathSciNet  MATH  Google Scholar 

  • [H] Ch. Hermite, Sur la fonction exponentielle, Oeuvres III, 150–181.

    Google Scholar 

  • [J] H. Jager, A multidimensional generalization of the Padé table, Thesis, University of Amsterdam (1964).

    Google Scholar 

  • [L] F. Lindemann, Ueber die Zahl π, Math. Ann. 20(1882), 213–225.

    Article  MathSciNet  Google Scholar 

  • [M] K. Mahler, Application of some formulae by Hermite to the approximation of exponentials and logarithms, Math. Ann. 168(1976), 200–227.

    Article  MathSciNet  MATH  Google Scholar 

  • [P] A.J. van der Poorten, A proof that Euler missed… Apéry's proof of the irrationality of ζ(3), Math. Intelligencer, 1(1978), 195–203.

    Article  MathSciNet  MATH  Google Scholar 

  • [R] E. Reyssat, Irrationalité de ζ(3) selon Apéry, Sém. Delange-Pisot-Poitou, 20e année, 1978/79, no 6.

    Google Scholar 

  • [Si1] C.L. Siegel, Transcendental Numbers (Princeton 1949).

    Google Scholar 

  • [Si2] C.L. Siegel, Die Gleichung axn−byn=c, Math. Ann. 114(1937), 57–68.

    Article  MathSciNet  Google Scholar 

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M. G. de Bruin H. van Rossum

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© 1981 Srpinger-Verlag

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Reukers, F. (1981). Pade-approximations in number theory. In: de Bruin, M.G., van Rossum, H. (eds) Padé Approximation and its Applications Amsterdam 1980. Lecture Notes in Mathematics, vol 888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095578

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  • DOI: https://doi.org/10.1007/BFb0095578

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11154-2

  • Online ISBN: 978-3-540-38606-3

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