A note on Beukers' integral

@article{Hata1995ANO,
  title={A note on Beukers' integral},
  author={Masayoshi Hata},
  journal={Journal of The Australian Mathematical Society},
  year={1995},
  volume={58},
  pages={143-153}
}
  • M. Hata
  • Published 1995
  • Mathematics
  • Journal of The Australian Mathematical Society
The aim of this note is to give a sharp lower bound for rational approximations to ζ(2) = π 2 /6 by using a specific Beukers' integral. Indeed, we will show that π 2 has an irrationality measure less than 6.3489, which improves the earlier result 7.325 announced by D. V. Chudnovsky and G. V. Chudnovsky. 
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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
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