Nous étudions un problème diophantien simultané relié à la conjecture de Littlewood. En utilisant des minorations connues de formes linéaires de logarithmes -adiques, nous montrons qu’un résultat que nous avons précédemment obtenu, concernant les nombres quadratiques, est presque optimal.
We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in -adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.
@article{JTNB_2005__17_1_207_0,
author = {de Mathan, Bernard},
title = {On a mixed {Littlewood} conjecture for quadratic numbers},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {207--215},
publisher = {Universit\'e Bordeaux 1},
volume = {17},
number = {1},
year = {2005},
doi = {10.5802/jtnb.487},
zbl = {1165.11325},
mrnumber = {2152221},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.487/}
}
TY - JOUR AU - de Mathan, Bernard TI - On a mixed Littlewood conjecture for quadratic numbers JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 207 EP - 215 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.487/ DO - 10.5802/jtnb.487 LA - en ID - JTNB_2005__17_1_207_0 ER -
%0 Journal Article %A de Mathan, Bernard %T On a mixed Littlewood conjecture for quadratic numbers %J Journal de théorie des nombres de Bordeaux %D 2005 %P 207-215 %V 17 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.487/ %R 10.5802/jtnb.487 %G en %F JTNB_2005__17_1_207_0
de Mathan, Bernard. On a mixed Littlewood conjecture for quadratic numbers. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 207-215. doi : 10.5802/jtnb.487. http://www.numdam.org/articles/10.5802/jtnb.487/
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