Abstract
At the “Journées Arithmétiques” held at Marseille-Luminy in June 1978, R. Apéry confronted his audience with a miraculous proof for the irrationality of ζ(3) = 1−3+2−3+3−3+... . The proof was elementary but the complexity and the unexpected nature of Apéry’s formulas divided the audience into believers and disbelievers. Everything turned out to be correct however. Two months later a complete exposition of the proof was presented at the International Congress of Mathematicians in Helsinki in August 1978 by H. Cohen. This proof was based on the lecture of Apéry, but contained ideas of Cohen and Don Zagier. For a more extensive record of this little history I refer to A. J. van der Poorten [1]. Apéry’s proof will be published in Acta Arithmetica.
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References
A.J. van der Poorten, “A proof that Euler missed ... Apery’s proof of the irrationality of (3)”. 7.
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© 1997 Springer Science+Business Media New York
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Beukers, F. (1997). A Note on the Irrationality of ζ(2) and ζ(3). In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2736-4_48
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DOI: https://doi.org/10.1007/978-1-4757-2736-4_48
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