A new irrationality measure for ζ(3)

• Autorzy: Masayoshi Hata
• Języki publikacji: EN

Kategorie tematyczne

• 11J82: Measures of irrationality and of transcendence

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 92
• Numer: 1
• Strony: 47-57

Daty

wydano

2000

otrzymano

1998-08-18

poprawiono

1999-07-08

Twórcy

autor

Masayoshi Hata

• Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-8501, Japan

Bibliografia

• [1] R. Apéry, Irrationalité de ζ(2) et ζ(3), Astérisque 61 (1979), 11-13.
• [2] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272.
• [3] R. Dvornicich and C. Viola, Some remarks on Beukers' integrals, in: Number Theory, Colloq. Math. Soc. János Bolyai 51, North-Holland, 1987, 637-657.
• [4] L. A. Gutnik, On the irrationality of some quantities containing ζ(3), Acta Arith. 42 (1983), 255-264 (in Russian); English transl.: Amer. Math. Soc. Transl. 140 (1988), 45-55.
• [5] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125.
• [6] M. Hata, A note on Beukers' integral, J. Austral. Math. Soc. Ser. A 58 (1995), 143-153.
• [7] Yu. V. Nesterenko, A few remarks on ζ(3), Mat. Zametki 59 (1996), 865-880 (in Russian); English transl.: Math. Notes 59 (1996), 625-636.
• [8] M. Prévost, A new proof of the irrationality of ζ(2) and ζ(3) using Padé approximants, J. Comput. Appl. Math. 67 (1996), 219-235.
• [9] V. N. Sorokin, Hermite-Padé approximations for Nikishin systems and the irrationality of ζ(3), Uspekhi Mat. Nauk 49 (1994), no. 2, 167-168 (in Russian); English transl.: Russian Math. Surveys 49 (1994), no. 2, 176-177.