On a permutation group related to ζ(2)

• Autorzy: Georges Rhin , Carlo Viola
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 77
• Numer: 1
• Strony: 23-56

Daty

wydano

1996

otrzymano

1995-09-19

poprawiono

1996-01-24

Twórcy

autor

Georges Rhin

• Département de Mathématiques, U.F.R. MIM, Université de Metz, Ile du Saulcy, 57045 Metz cedex 1, France

autor

Carlo Viola

• Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

Bibliografia

• [1] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272.
• [2] A. C. Dixon, On a certain double integral, Proc. London Math. Soc. (2) 2 (1905), 8-15.
• [3] R. Dvornicich and C. Viola, Some remarks on Beukers' integrals, in: Colloq. Math. Soc. János Bolyai 51, Budapest, 1987, 637-657.
• [4] A. Erdélyi et al., Higher Transcendental Functions (Bateman Manuscript Project), Vol. 1, McGraw-Hill, New York, 1953.
• [5] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125.
• [6] M. Hata, Rational approximations to π and some other numbers, Acta Arith. 63 (1993), 335-349.
• [7] M. Hata, A note on Beukers' integral, J. Austral. Math. Soc. A 58 (1995), 143-153.
• [8] G. Rhin and C. Viola, On the irrationality measure of ζ(2), Ann. Inst. Fourier (Grenoble) 43 (1993), 85-109.
• [9] E. A. Rukhadze, A lower bound for the approximation of ln 2 by rational numbers, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987 (6), 25-29 (in Russian).