Non-integrability of the equations of heavy gyrostat

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.

Irrationality results for theta functions by Gel'fond-Schneider's method

Michel Waldschmidt, Peter Bundschuh (1989)

Acta Arithmetica

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On a question of Lehmer and the number of irreducible factors of a polynomial

Edward Dobrowolski (1979)

Acta Arithmetica

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