Irrationality of values of the Riemann zeta function

@article{Zudilin2002IrrationalityOV,
  title={Irrationality of values of the Riemann zeta function},
  author={W. Zudilin},
  journal={Izvestiya: Mathematics},
  year={2002},
  volume={66},
  pages={489-542}
}
  • W. Zudilin
  • Published 2002
  • Mathematics
  • Izvestiya: Mathematics
  • The paper deals with a generalization of Rivoal's construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function ζ(s) only at odd points. We prove theorems on the irrationality of the number ζ(s) for some odd integers s in a given segment of the set of positive integers. Using certain refined arithmetical estimates, we strengthen Rivoal's original results on the linear independence of the ζ(s). 
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    References

    SHOWING 1-10 OF 56 REFERENCES
    A few remarks on ζ(3)
    • 50
    A Note on the Irrationality of ζ(2) and ζ(3)
    • 233
    The group structure for ζ(3)
    • 68
    • PDF
    Introduction to Modular Forms
    • 169
    Irrationalité de ζ(2) et ζ(3)
    • Astérisque 61
    • 1979
    Asymptotic methods in analysis
    • 916
    • Highly Influential