On the irrationality measure of \(\zeta (2)\) (Q1210516)

The authors provide an effective irrationality measure \(7.398\ldots\) for \(\zeta(2)\). This implies the irrationality measure \(14.796\ldots\) for \(\pi\). To obtain this measure the authors construct a sequence of approximations via integrals of the form \(\int_ 0^ 1\int_ 0^ 1 H(x,y)(1-xy)^{-n-1} dx dy\). The main part of the paper is devoted to the study of the asymptotics of this integral and to an optimal choice for \(H(x,y)\). In [Acta Arith. 63, 335-349 (1993; Zbl 0776.11033)]\textit{M. Hata} gives the irrationality measure \(8.0161\) using an entirely different method.