Skip to main content
SpringerLink
Log in

Diophantine properties of numbers related to Catalan's constant

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Apéry, R.: Irrationalité de ζ(2) et ζ(3). Astérisque 61, 11–13 (1979)

    Google Scholar 

  2. Bailey, W.N.: Generalized hypergeometric series, Cambridge Math. Tracts 32 (Cambridge University Press, Cambridge 1935); 2nd reprinted edition (Stechert-Hafner, New York 1964)

  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))

  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)

    Article  MATH  Google Scholar 

  5. Hata, M.: Legendre type polynomials and irrationality measures. J. Reine Angew. Math. 407, 99–125 (1990)

    MathSciNet  MATH  Google Scholar 

  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)

  7. Rhin, G., Viola, C.: On a permutation group related to~ζ(2). Acta Arith. 77, 23–56 (1996)

    MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. Slater, L.J.: Generalized hypergeometric functions, 2nd edition (Cambridge University Press, Cambridge 1966)

  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. Zudilin, W.: Arithmetic of linear forms involving odd zeta values, Preprint (August 2001); E-print math.NT/0206176, 42~pages (2002)

  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. Zudilin, W.: Apéry-like difference equation for Catalan's constant, E-print math.NT/0201024, 10~pages (2002)

Download references

Author information

Author notes

  1. T. Rivoal

    Present address: LMNO, CNRS UMR 6139, Université de Caen, BP 5186, 14032, Caen cedex, France

Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, CNRS UMR 7586, Théorie des Nombres, case 247, 175, rue du Chevaleret, 75013, Paris, France

    T. Rivoal

  2. Department of Mechanics and Mathematics, Moscow Lomonosov State University, Vorobiovy Gory, GSP-2, 119992, Moscow, Russia

    W. Zudilin

Authors
  1. T. Rivoal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Zudilin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Rivoal.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-003-0420-2

Keywords

Search

Navigation