A new irrationality measure for ζ(3)

Acta Arithmetica

Volumn 92, Issue 1, 2000, Pages 47-57

  Hata, Masayoshi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034366259     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-92-1-47-57     Document Type: Article

References (12)

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. 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.
6. M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125.
7. -, A note on Beukers' integral, J. Austral. Math. Soc. Ser. A 58 (1995), 143-153.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.