Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques

Guy Diaz

Acta Arithmetica (1993)

  • Volume: 64, Issue: 1, page 43-57
  • ISSN: 0065-1036

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Guy Diaz. "Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques." Acta Arithmetica 64.1 (1993): 43-57. <http://eudml.org/doc/206534>.

@article{GuyDiaz1993,
author = {Guy Diaz},
journal = {Acta Arithmetica},
keywords = {explicit lower bounds; transcendence measure; logarithms; exponentials},
language = {fre},
number = {1},
pages = {43-57},
title = {Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques},
url = {http://eudml.org/doc/206534},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Guy Diaz
TI - Une nouvelle minoration de |logα - β|, |α - expβ|, α et β algébriques
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 1
SP - 43
EP - 57
LA - fre
KW - explicit lower bounds; transcendence measure; logarithms; exponentials
UR - http://eudml.org/doc/206534
ER -

References

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  1. [Ch] G. V. Chudnovsky, Contributions to the Theory of Transcendental Numbers, Math. Surveys Monographs 19, Amer. Math. Soc., 1984. 
  2. [Ci] P. L. Cijsouw, Transcendence measures of exponentials and logarithms of algebraic numbers, Compositio Math. 28 (1974), 163-178. Zbl0284.10013
  3. [Di] G. Diaz, Complément à : Sur l'approximation de π par des nombres algébriques particuliers, Compositio Math. 79 (1991), 255-270. Zbl0734.11038
  4. [Du] A. Durand, Simultaneous diophantine approximations and Hermite's method, Bull. Austral. Math. Soc. 21 (1980), 463-470. Zbl0421.10020
  5. [F] N. I. Feldman, On the problem of the measure of transcendence of e, Uspekhi Mat. Nauk 18 (3) (1963), 207-213 (in Russian). 
  6. [FS] N. I. Feldman and A. B. Shidlovskiĭ, The development and present state of the theory of transcendental numbers, Russian Math. Surveys 22 (3) (1967), 1-79. 
  7. [G] A. I. Galochkin, On the diophantine approximation of values of the exponential function and of solutions of some transcendental equations, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1972 (3), 16-23. 
  8. [M1] K. Mahler, Zur approximation der Exponentialfunktion und der Logarithmus, J. Reine Angew. Math. 166 (1932), 118-150. Zbl0003.38805
  9. [M2] K. Mahler, Lectures on Transcendental Numbers, Lecture Notes in Math. 546, Springer, 1976. 
  10. [P] P. Philippon, Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France 114 (1986), 355-383; errata et addenda, Bull. Soc. Math. France 115 (1987), 397-398. Zbl0617.14001
  11. [R] K. Ramachandra, An easy transcendence measure for e, J. Indian Math. Soc. 51 (1987), 111-116. Zbl0669.10058
  12. [S] T. Schneider, Introduction aux nombres transcendants, Gauthier-Villars, 1959. Zbl0098.26304
  13. [W1] M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257-283. Zbl0357.10017
  14. [W2] M. Waldschmidt, Transcendence measures for exponentials and logarithms, J. Austral. Math. Soc. Ser. A 25 (1978), 445-465. Zbl0388.10022
  15. [W3] M. Waldschmidt, Transcendance et exponentielles en plusieurs variables, Invent. Math. 63 (1981), 97-127. Zbl0454.10020
  16. [W4] M. Waldschmidt, Nouvelles méthodes pour minorer des combinaisons linéaires de logarithmes de nombres algébriques, Sem. Théorie des Nombres de Bordeaux 3 (1991), 129-185. Zbl0733.11020

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