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

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.

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.

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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. http://www.numdam.org/articles/10.5802/aif.1322/

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