A new irrationality measure for ζ(3)
Masayoshi Hata
Acta Arithmetica, Tome 92 (2000), p. 47-57 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:207368
@article{bwmeta1.element.bwnjournal-article-aav92i1p47bwm,
     author = {Masayoshi Hata},
     title = {A new irrationality measure for $\zeta$(3)},
     journal = {Acta Arithmetica},
     volume = {92},
     year = {2000},
     pages = {47-57},
     zbl = {0955.11023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav92i1p47bwm}
}
Masayoshi Hata. A new irrationality measure for ζ(3). Acta Arithmetica, Tome 92 (2000) pp. 47-57. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav92i1p47bwm/

[000] [1] R. Apéry, Irrationalité de ζ(2) et ζ(3), Astérisque 61 (1979), 11-13.

[001] [2] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272.

[002] [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. | Zbl 0755.11019

[003] [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. | Zbl 0474.10026

[004] [5] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125. | Zbl 0692.10034

[005] [6] M. Hata, A note on Beukers' integral, J. Austral. Math. Soc. Ser. A 58 (1995), 143-153. | Zbl 0830.11026

[006] [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.

[007] [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.

[008] [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.