In this paper we prove a lower bound for the linear dependence of three positive rational numbers under certain weak linear independence conditions on the coefficients of the linear forms. Let with positive integers and positive multiplicatively independent rational numbers greater than . Let with coprime positive integers . Let and assume that gcd Let
Dans cet article, nous donnons une minoration de la dépendance linéaire de trois nombres rationnels positifs valable sous certaines conditions faibles d’indépendance linéaire des coefficients des formes linéaires. Soit avec des entiers positifs et des rationnels multiplicativement indépendants supérieurs à . Soit où sont des entiers positifs premiers entre eux Soit et supposons que pgcd Soit
@article{JTNB_1997__9_1_97_0, author = {Curtis D. Bennett and Josef Blass and A. M. W. Glass and David B. Meronk and Ray P. Steiner}, title = {Linear forms in the logarithms of three positive rational numbers}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {97--136}, publisher = {Universit\'e Bordeaux I}, volume = {9}, number = {1}, year = {1997}, zbl = {0905.11032}, mrnumber = {1469664}, language = {en}, url = {https://jtnb.centre-mersenne.org/item/JTNB_1997__9_1_97_0/} }
TY - JOUR AU - Curtis D. Bennett AU - Josef Blass AU - A. M. W. Glass AU - David B. Meronk AU - Ray P. Steiner TI - Linear forms in the logarithms of three positive rational numbers JO - Journal de théorie des nombres de Bordeaux PY - 1997 SP - 97 EP - 136 VL - 9 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/item/JTNB_1997__9_1_97_0/ LA - en ID - JTNB_1997__9_1_97_0 ER -
%0 Journal Article %A Curtis D. Bennett %A Josef Blass %A A. M. W. Glass %A David B. Meronk %A Ray P. Steiner %T Linear forms in the logarithms of three positive rational numbers %J Journal de théorie des nombres de Bordeaux %D 1997 %P 97-136 %V 9 %N 1 %I Université Bordeaux I %U https://jtnb.centre-mersenne.org/item/JTNB_1997__9_1_97_0/ %G en %F JTNB_1997__9_1_97_0
Curtis D. Bennett; Josef Blass; A. M. W. Glass; David B. Meronk; Ray P. Steiner. Linear forms in the logarithms of three positive rational numbers. Journal de théorie des nombres de Bordeaux, Volume 9 (1997) no. 1, pp. 97-136. https://jtnb.centre-mersenne.org/item/JTNB_1997__9_1_97_0/
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