Une version quantitative du théorème de Lindemann-Weierstrass

Mohammed Ably

Acta Arithmetica (1994)

  • Volume: 67, Issue: 1, page 29-45
  • ISSN: 0065-1036

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Mohammed Ably. "Une version quantitative du théorème de Lindemann-Weierstrass." Acta Arithmetica 67.1 (1994): 29-45. <http://eudml.org/doc/206616>.

@article{MohammedAbly1994,
author = {Mohammed Ably},
journal = {Acta Arithmetica},
keywords = {Lindemann-Weierstrass theorem; height; Gel'fond's method; Philippon's criterion; algebraic independence},
language = {fre},
number = {1},
pages = {29-45},
title = {Une version quantitative du théorème de Lindemann-Weierstrass},
url = {http://eudml.org/doc/206616},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Mohammed Ably
TI - Une version quantitative du théorème de Lindemann-Weierstrass
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 1
SP - 29
EP - 45
LA - fre
KW - Lindemann-Weierstrass theorem; height; Gel'fond's method; Philippon's criterion; algebraic independence
UR - http://eudml.org/doc/206616
ER -

References

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  1. [D] G. Diaz, Grands degrés de transcendance pour des familles d'exponentielles, J. Number Theory 31 (1989), 1-23. Zbl0661.10047
  2. [J] E. M. Jabbouri, Sur un critère d'indépendance algébrique de P. Philippon, dans : Approximations diophantiennes et nombres transcendants, Luminy 1990, P. Philippon (éd.), Walter de Gruyter, 1992, 195-202. 
  3. [M] K. Mahler, Zur Approximation der Exponential Funktion und des Logarithmus I, J. Reine Angew. Math. 166 (1932), 118-136. Zbl57.0242.03
  4. [N₁] Yu. V. Nesterenko, Estimates for the orders of zeros of functions of a certain class and their applications in the theory of transcendental numbers, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 253-284 (en russe); trad. anglaise: Math. USSR-Izv. 11 (1977). 
  5. [N₂] Yu. V. Nesterenko, On algebraic independence of algebraic powers of algebraic numbers, Mat. Sb. 123 (165) (1984), 435-459 (en russe); trad. anglaise: Math. USSR-Sb. 51 (1985). 
  6. [N₃] Yu. V. Nesterenko, On a measure of algebraic independence of the values of elliptic functions, dans : Approximations diophantiennes et nombres transcendants, Luminy 1990, P. Philippon (éd.), Walter de Gruyter, 1992, 239-248. 
  7. [P₁] P. Philippon, Critères pour l'indépendance algébrique, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 5-52. 
  8. [P₂] P. Philippon, Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France 114 (1986), 335-383. Zbl0617.14001
  9. [R] E. Reyssat, Approximation algébrique de nombres liés aux fonctions elliptiques, Bull. Soc. Math. France 108 (1980), 47-79. Zbl0432.10018
  10. [S] C. Siegel, Transcendental Numbers, Ann. of Math. Stud., Princeton, 1949. 
  11. [T] T. Töpfer, Über lineare Unabhängigkeit in algebraischen Zahlkörpern, à paraître. 
  12. [Wa₁] M. Waldschmidt, Nombres transcendants et groupes algébriques, Astérisque 69-70 (1979). 
  13. [Wa₂] M. Waldschmidt, Nombres transcendants, Lecture Notes in Math. 402, Springer, 1974. Zbl0302.10030

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