On the irrationality measure of ζ(2)
Annales de l'Institut Fourier, Tome 43 (1993) no. 1, p. 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 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 2 . The numerical results are obtained with the aid of a semi-infinite linear programming method.
@article{AIF_1993__43_1_85_0,
     author = {Rhin, Georges and Viola, Carlo},
     title = {On the irrationality measure of $\zeta (2)$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {43},
     number = {1},
     year = {1993},
     pages = {85-109},
     doi = {10.5802/aif.1322},
     mrnumber = {1209696},
     zbl = {0776.11036},
     mrnumber = {94b:11065},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1993__43_1_85_0}
}
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/item/AIF_1993__43_1_85_0/

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