Two hypergeometric tales and a new irrationality measure of $$\zeta (2)$$ζ(2)

@article{Zudilin2013TwoHT,
  title={Two hypergeometric tales and a new irrationality measure of \$\$\zeta (2)\$\$$\zeta$(2)},
  author={W. Zudilin},
  journal={Annales math{\'e}matiques du Qu{\'e}bec},
  year={2013},
  volume={38},
  pages={101-117}
}
  • W. Zudilin
  • Published 2013
  • Mathematics
  • Annales mathématiques du Québec
We prove the new upper bound $$5.095412$$5.095412 for the irrationality exponent of $$\zeta (2)=\pi ^2/6$$ζ(2)=π2/6; the earlier record bound $$5.441243$$5.441243 was established in 1996 by G. Rhin and C. Viola.RésuméNous obtenons une nouvelle borne pour l’exposant d’irrationnalité de $$\zeta (2)=\pi ^2/6$$ζ(2)=π2/6, à savoir $$5.095412$$5.095412, cette dernière améliorant le record $$5.441243$$5.441243 établi par G. Rhin et C. Viola. 
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Irrationality proofs for zeta values, moduli spaces and dinner parties
Hypergeometric rational approximations to ζ(4)
Hypergeometric heritage of W. N. Bailey

References

SHOWING 1-10 OF 24 REFERENCES
The group structure for ζ(3)
Ramanujan-type formulae and irrationality measures of some multiples of $ {\pi}$
Arithmetic of linear forms involving odd zeta values
Irrationality of values of the Riemann zeta function
Generalized hypergeometric series
WZ-proofs of "divergent" Ramanujan-type series
A few remarks on ζ(3)
...
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2
3
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