Pour un entier strictement positif et un nombre réel , on note le supremum des nombres réels pour lesquels il existe des entiers arbitrairement grands tels que sont tous inférieurs à . Ici, désigne la distance à l’entier le plus proche. Nous étudions l’ensemble des valeurs prises par la function et, plus généralement, nous nous intéressons au spectre de . Nous formulons également plusieurs problèmes ouverts.
For a positive integer and a real number , let denote the supremum of the real numbers such that there are arbitrarily large positive integers such that are all less than . Here, denotes the distance to the nearest integer. We study the set of values taken by the function and, more generally, we are concerned with the joint spectrum of . We further address several open problems.
@article{AIF_2010__60_6_2165_0, author = {Bugeaud, Yann}, title = {On simultaneous rational approximation to a real number and its integral powers}, journal = {Annales de l'Institut Fourier}, volume = {60}, year = {2010}, pages = {2165-2182}, doi = {10.5802/aif.2580}, zbl = {1229.11100}, mrnumber = {2791654}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2010__60_6_2165_0} }
Bugeaud, Yann. On simultaneous rational approximation to a real number and its integral powers. Annales de l'Institut Fourier, Tome 60 (2010) pp. 2165-2182. doi : 10.5802/aif.2580. http://gdmltest.u-ga.fr/item/AIF_2010__60_6_2165_0/
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