Mathematische Annalen

, Volume 326, Issue 4, pp 705–721 | Cite as

Diophantine properties of numbers related to Catalan's constant

  • T. Rivoal
  • W. Zudilin


Diophantine Property 
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  1. 1.
    Apéry, R.: Irrationalité de ζ(2) et ζ(3). Astérisque 61, 11–13 (1979)Google Scholar
  2. 2.
    Bailey, W.N.: Generalized hypergeometric series, Cambridge Math. Tracts 32 (Cambridge University Press, Cambridge 1935); 2nd reprinted edition (Stechert-Hafner, New York 1964)Google Scholar
  3. 3.
    Baker, A.: The theory of linear forms in logarithms, Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976), pp. 1–27 (Academic Press, London (1977))Google Scholar
  4. 4.
    Ball, K., Rivoal, T.: Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs. Invent. Math. 146(1), 193–207 (2001)CrossRefzbMATHGoogle Scholar
  5. 5.
    Hata, M.: Legendre type polynomials and irrationality measures. J. Reine Angew. Math. 407, 99–125 (1990)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Nesterenko, Yu.V.: On the linear independence of numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 46–54 (1985); English transl., Moscow Univ. Math. Bull. 40, 69–74 (1985)Google Scholar
  7. 7.
    Rhin, G., Viola, C.: On a permutation group related to~ζ(2). Acta Arith. 77, 23–56 (1996)zbMATHGoogle Scholar
  8. 8.
    Rivoal, T.: La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs. C.R. Acad. Sci. Paris Sér. I Math. 331, 267–270 (2000)CrossRefzbMATHGoogle Scholar
  9. 9.
    Rivoal, T.: Irrationalité d'au moins un des neuf nombres ζ(5),ζ(7),…,ζ(21), Acta Arith. 103, 157–167 (2002)Google Scholar
  10. 10.
    Slater, L.J.: Generalized hypergeometric functions, 2nd edition (Cambridge University Press, Cambridge 1966)Google Scholar
  11. 11.
    Zudilin, W.: Irrationality of values of Riemann's zeta function, Izv. Ross. Akad. Nauk Ser. Mat. 66, 49–102 (2002); English transl., Russian Acad. Sci. Izv. Math. 66, (2002)Google Scholar
  12. 12.
    Zudilin, W.: Arithmetic of linear forms involving odd zeta values, Preprint (August 2001); E-print math.NT/0206176, 42~pages (2002)Google Scholar
  13. 13.
    Zudilin, V.V.: One of the numbers ζ(5),ζ(7),ζ(9),ζ(11) is irrational, Uspekhi Mat. Nauk 56(4), 149–150 (2001); English transl., Russian Math. Surveys 56, 774–776 (2001)Google Scholar
  14. 14.
    Zudilin, W.: Apéry-like difference equation for Catalan's constant, E-print math.NT/0201024, 10~pages (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuCNRS UMR 7586, Théorie des Nombres, case 247ParisFrance
  2. 2.Department of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia
  3. 3.LMNO, CNRS UMR 6139Université de CaenCaen cedexFrance

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