no. 1
On the irrationality measure of ζ(2)
Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 85-109

We prove that 7. 398 537 is an irrationality measure of ζ(2)=π 2 /6. We employ double integrals of suitable rational functions invariant under a group of birational transformations of ℂ 2 . The numerical results are obtained with the aid of a semi-infinite linear programming method.

On démontre que 7. 398 537 est une mesure d’irrationalité de ζ(2)=π 2 /6. On utilise des intégrales doubles de fonctions rationnelles stables par un groupe de transformations birationnelles de ℂ 2 . Les résultats numériques sont obtenus à l’aide d’une méthode de programmation linéaire semi-infinie.

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     title = {On the irrationality measure of $\zeta (2)$},
     journal = {Annales de l'Institut Fourier},
     pages = {85--109},
     year = {1993},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
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     doi = {10.5802/aif.1322},
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Rhin, Georges; Viola, Carlo. On the irrationality measure of $\zeta (2)$. Annales de l'Institut Fourier, Tome 43 (1993) no. 1, pp. 85-109. doi: 10.5802/aif.1322

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