Rational approximations to π and some other numbers

@article{Hata1993RationalAT,
  title={Rational approximations to $\pi$ and some other numbers},
  author={M. Hata},
  journal={Acta Arithmetica},
  year={1993},
  volume={63},
  pages={335-349}
}
  • M. Hata
  • Published 1993
  • Mathematics
  • Acta Arithmetica
Analytic number theory and approximation
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Abstract We give a sharp lower bound for rational approximations to π by modifying the classical approximation formula to the system {(log(1 − x )) j } 1 ≤ j ≤ K due to Hermite. In fact, it will heExpand
Approximants de Padé et mesures effectives d’irrationalité
Les approximants de Pade; des fonctions hypergeometriques ont ete utilises pour l’etude en des points rationnels z=p/q des approximations diophantiennes des valeurs de ces fonctions. Cette methodeExpand
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At the “Journees Arithmetiques” held at Marseille-Luminy in June 1978, R. Apery confronted his audience with a miraculous proof for the irrationality of ζ(3) = l-3+ 2-3+ 3-3 + .... The proof wasExpand
On the Approximation of π
The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of π from a given rational or algebraic number.