This article is cited in 24 papers

A transcendence measure for $\pi^2$

V. N. Sorokin

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 517.5

MSC: 11J82, 41A21

Received: 13.11.1995

DOI: 10.4213/sm179

 English version: Sbornik: Mathematics, 1996, 187:12, 1819–1852

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