A new irrationality measure for ζ(3)

Masayoshi Hata

Acta Arithmetica (2000)

  • Volume: 92, Issue: 1, page 47-57
  • ISSN: 0065-1036

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Masayoshi Hata. "A new irrationality measure for ζ(3)." Acta Arithmetica 92.1 (2000): 47-57. <http://eudml.org/doc/207368>.

@article{MasayoshiHata2000,
author = {Masayoshi Hata},
journal = {Acta Arithmetica},
keywords = {Riemann zeta-function; irrationality measure; Legendre-type polynomials},
language = {eng},
number = {1},
pages = {47-57},
title = {A new irrationality measure for ζ(3)},
url = {http://eudml.org/doc/207368},
volume = {92},
year = {2000},
}

TY - JOUR
AU - Masayoshi Hata
TI - A new irrationality measure for ζ(3)
JO - Acta Arithmetica
PY - 2000
VL - 92
IS - 1
SP - 47
EP - 57
LA - eng
KW - Riemann zeta-function; irrationality measure; Legendre-type polynomials
UR - http://eudml.org/doc/207368
ER -

References

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  1. [1] R. Apéry, Irrationalité de ζ(2) et ζ(3), Astérisque 61 (1979), 11-13. 
  2. [2] F. Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268-272. 
  3. [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. Zbl0755.11019
  4. [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. Zbl0474.10026
  5. [5] M. Hata, Legendre type polynomials and irrationality measures, J. Reine Angew. Math. 407 (1990), 99-125. Zbl0692.10034
  6. [6] M. Hata, A note on Beukers' integral, J. Austral. Math. Soc. Ser. A 58 (1995), 143-153. Zbl0830.11026
  7. [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. [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. [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. 

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