Article PDF
Avoid common mistakes on your manuscript.
References
Apéry, R.: Irrationalité de ζ(2) et ζ(3). Astérisque 61, 11–13 (1979)
Bailey, W.N.: Generalized hypergeometric series, Cambridge Math. Tracts 32 (Cambridge University Press, Cambridge 1935); 2nd reprinted edition (Stechert-Hafner, New York 1964)
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))
Ball, K., Rivoal, T.: Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs. Invent. Math. 146(1), 193–207 (2001)
Hata, M.: Legendre type polynomials and irrationality measures. J. Reine Angew. Math. 407, 99–125 (1990)
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)
Rhin, G., Viola, C.: On a permutation group related to~ζ(2). Acta Arith. 77, 23–56 (1996)
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)
Rivoal, T.: Irrationalité d'au moins un des neuf nombres ζ(5),ζ(7),…,ζ(21), Acta Arith. 103, 157–167 (2002)
Slater, L.J.: Generalized hypergeometric functions, 2nd edition (Cambridge University Press, Cambridge 1966)
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)
Zudilin, W.: Arithmetic of linear forms involving odd zeta values, Preprint (August 2001); E-print math.NT/0206176, 42~pages (2002)
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)
Zudilin, W.: Apéry-like difference equation for Catalan's constant, E-print math.NT/0201024, 10~pages (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rivoal, T., Zudilin, W. Diophantine properties of numbers related to Catalan's constant. Math. Ann. 326, 705–721 (2003). https://doi.org/10.1007/s00208-003-0420-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-003-0420-2