Nous donnons une minoration explicite pour les formes linéaires en deux logarithmes. Pour cela nous spécialisons la méthode de Schneider avec multiplicité décrite dans [10]. Nous améliorons substantiellement les constantes numériques intervenant dans les énoncés existants pour le cas de deux logarithmes, obtenus avec la méthode de Baker ou bien celle de Schneider avec multiplicité. Notre constante est de l’ordre de
We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in [10]. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around
@article{JTNB_2006__18_1_125_0,
author = {Nicolas Gouillon},
title = {Explicit lower bounds for linear forms in two logarithms},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {125--146},
publisher = {Universit\'e Bordeaux 1},
volume = {18},
number = {1},
year = {2006},
doi = {10.5802/jtnb.537},
mrnumber = {2245879},
zbl = {05070451},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.537/}
}
TY - JOUR AU - Nicolas Gouillon TI - Explicit lower bounds for linear forms in two logarithms JO - Journal de théorie des nombres de Bordeaux PY - 2006 SP - 125 EP - 146 VL - 18 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.537/ DO - 10.5802/jtnb.537 LA - en ID - JTNB_2006__18_1_125_0 ER -
%0 Journal Article %A Nicolas Gouillon %T Explicit lower bounds for linear forms in two logarithms %J Journal de théorie des nombres de Bordeaux %D 2006 %P 125-146 %V 18 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.537/ %R 10.5802/jtnb.537 %G en %F JTNB_2006__18_1_125_0
Nicolas Gouillon. Explicit lower bounds for linear forms in two logarithms. Journal de théorie des nombres de Bordeaux, Tome 18 (2006) no. 1, pp. 125-146. doi : 10.5802/jtnb.537. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.537/
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