Geodesic
A transcendence measure for $\pi^2$
Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1819-1852

Voir la notice de l'article provenant de la source Math-Net.Ru

A new proof of the fact that $\pi^2$ is transcendental is proposed. A modification of Hermite's method for an expressly constructed Nikishin system is used. The Beukers integral, which was previously used to prove Apéry's theorem on the irrationality of $\zeta (2)$ and $\zeta (3)$ is a special case of this construction. 
@article{SM_1996_187_12_a3,
     author = {V. N. Sorokin},
     title = {A transcendence measure for $\pi^2$},
     journal = {Sbornik. Mathematics},
     pages = {1819--1852},
     publisher = {mathdoc},
     volume = {187},
     number = {12},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_12_a3/}
}
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V. N. Sorokin. A transcendence measure for $\pi^2$. Sbornik. Mathematics, Tome 187 (1996) no. 12, pp. 1819-1852. http://geodesic.mathdoc.fr/item/SM_1996_187_12_a3/