# 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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