On the irrationality measure of ζ(2)
Rhin, Georges ; Viola, Carlo
Annales de l'Institut Fourier, Tome 43 (1993), p. 85-109 / Harvested from Numdam
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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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     author = {Rhin, Georges and Viola, Carlo},
     title = {On the irrationality measure of $\zeta (2)$},
     journal = {Annales de l'Institut Fourier},
     volume = {43},
     year = {1993},
     pages = {85-109},
     doi = {10.5802/aif.1322},
     mrnumber = {94b:11065},
     zbl = {0776.11036},
     mrnumber = {1209696},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1993__43_1_85_0}
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Rhin, Georges; Viola, Carlo. On the irrationality measure of $\zeta (2)$. Annales de l'Institut Fourier, Tome 43 (1993) pp. 85-109. doi : 10.5802/aif.1322. http://gdmltest.u-ga.fr/item/AIF_1993__43_1_85_0/

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