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.
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.
@article{JTNB_2005__17_1_207_0, author = {Bernard de Mathan}, 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 = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.487/} }
TY - JOUR TI - On a mixed Littlewood conjecture for quadratic numbers JO - Journal de Théorie des Nombres de Bordeaux PY - 2005 DA - 2005/// SP - 207 EP - 215 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.487/ UR - https://zbmath.org/?q=an%3A1165.11325 UR - https://www.ams.org/mathscinet-getitem?mr=2152221 UR - https://doi.org/10.5802/jtnb.487 DO - 10.5802/jtnb.487 LA - en ID - JTNB_2005__17_1_207_0 ER -
Bernard de Mathan. On a mixed Littlewood conjecture for quadratic numbers. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 207-215. doi : 10.5802/jtnb.487. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.487/
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