Sur l’approximation de π par des nombres algébriques particuliers

Guy Diaz

Compositio Mathematica (1990)

  • Volume: 74, Issue: 3, page 285-298
  • ISSN: 0010-437X

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Diaz, Guy. "Sur l’approximation de $\pi $ par des nombres algébriques particuliers." Compositio Mathematica 74.3 (1990): 285-298. <http://eudml.org/doc/90022>.

@article{Diaz1990,
author = {Diaz, Guy},
journal = {Compositio Mathematica},
keywords = {approximation by algebraic numbers; cyclotomic fields; logarithmic Weil height; lower bound},
language = {fre},
number = {3},
pages = {285-298},
publisher = {Kluwer Academic Publishers},
title = {Sur l’approximation de $\pi $ par des nombres algébriques particuliers},
url = {http://eudml.org/doc/90022},
volume = {74},
year = {1990},
}

TY - JOUR
AU - Diaz, Guy
TI - Sur l’approximation de $\pi $ par des nombres algébriques particuliers
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 74
IS - 3
SP - 285
EP - 298
LA - fre
KW - approximation by algebraic numbers; cyclotomic fields; logarithmic Weil height; lower bound
UR - http://eudml.org/doc/90022
ER -

References

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  1. [1] Cijsouw, P.L., A transcendence measure for π, in "Transcendence Theory: Advances and Applications" (edited by A. Baker, D. W. Masser), Academic Press, 1977, 93-100. Zbl0361.10029
  2. [2] Feldman, N.I., Approximation of number π by algebraic numbers from special fields. J. Number Theory9 (1977) 48-60. Zbl0345.10018
  3. [3] Mignotte, M. et Waldschmidt, M., Approximation des valeurs de fonctions transcendantes. Indag. Math.37(1975) 213-223. Zbl0305.10027MR376552
  4. [4] Mignotte, M. et Waldschmidt, M., Approximation simultanée de valeurs de la fonction exponentielle. Compositio Math.34 (1977) 127-139. Zbl0345.10022MR441884
  5. [5] Mignotte, M. et Waldschmidt, M.: Linear forms in two logarithms and Schneider's method III. Ann. Fac. Sci. Toulouse Math. (à paraître). Zbl0702.11044
  6. [6] Philippon, P., Polynôme d'interpolation sur Z et Z[i]. Actes du colloque A. Durand (I.H.P.1988) (à paraître). Zbl0701.11023
  7. [7] Philippon, P., Lemmes de zéros dans les groupes algébriques commutatifs. Bull. Soc. Math. France114(1986) 355-383. Zbl0617.14001MR878242
  8. [8] Rosser, J.B. et Schoenfeld, L., Sharper bounds for the Chebyshev functions θ(x), ϕ(x). Math. Comp.29(1975) 243-269. Zbl0295.10036
  9. [9] Waldschmidt, M., Nombres transcendants. Lecture Notes in Math. 402, Springer, 1974. Zbl0302.10030MR360483
  10. [10] Waldschmidt, M., Transcendence measures for exponentials and logarithms. J. Austral. Math. Soc. Ser.A, 25(1978)445-465. Zbl0388.10022MR508469
  11. [11] Waldschmidt, M., A lower bound for linear forms in logarithms. Acta Arith.37(1980) 257-283. Zbl0357.10017MR598881
  12. [12] Waldschmidt, M., Transcendance et exponentielles en plusieurs variables. Invent. Math.63 (1981) 97-127. Zbl0454.10020MR608530

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