On démontre que 7. 398 537 est une mesure d’irrationalité de . On utilise des intégrales doubles de fonctions rationnelles stables par un groupe de transformations birationnelles de . 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 . We employ double integrals of suitable rational functions invariant under a group of birational transformations of . 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}, pages = {85--109}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {43}, number = {1}, year = {1993}, doi = {10.5802/aif.1322}, zbl = {0776.11036}, mrnumber = {1209696}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1322/} }
TY - JOUR AU - Rhin, Georges AU - Viola, Carlo TI - On the irrationality measure of $\zeta (2)$ JO - Annales de l'Institut Fourier PY - 1993 SP - 85 EP - 109 VL - 43 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1322/ DO - 10.5802/aif.1322 LA - en ID - AIF_1993__43_1_85_0 ER -
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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