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A note on Beukers' integral

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

Masayoshi Hata
Masayoshi Hata
Affiliation:
Institute of Mathematics, Yoshida College, Kyoto University
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Abstract

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The aim of this note is to give a sharp lower bound for rational approximations to ζ(2) = π2/6 by using a specific Beukers' integral. Indeed, we will show that π2 has an irrationality measure less than 6.3489, which improves the earlier result 7.325 announced by D. V. Chudnovsky and G. V. Chudnovsky.

MSC classification

Secondary: 11J82: Measures of irrationality and of transcendence
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 58 , Issue 2 , April 1995 , pp. 143 - 153
Copyright
Copyright © Australian Mathematical Society 1995

References

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