En utilisant à la fois la théorie des polynômes orthogonaux et des arguments élémentaires de géométrie des nombres, nous donnons ici des nouveaux encadrements pour le diamètre transfini entier d’un intervalle d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de et des dénominateurs de ses extrémités.
Some new upper and lower bound for the least deviation from zero of integral polynomials over intervals with rational extremities are given. These bounds, obtained combining the theory of orthogonal polynomials with elementary arguments from the geometry of numbers, explicitly depend on the diameter of and on the denominators of its extremities.
@article{AIF_1990__40_4_885_0,
author = {Amoroso, Francesco},
title = {Sur le diam\`etre transfini entier d'un intervalle r\'eel},
journal = {Annales de l'Institut Fourier},
pages = {885--911},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {40},
number = {4},
year = {1990},
doi = {10.5802/aif.1240},
zbl = {0713.41004},
mrnumber = {1096596},
language = {fr},
url = {http://www.numdam.org/articles/10.5802/aif.1240/}
}
TY - JOUR AU - Amoroso, Francesco TI - Sur le diamètre transfini entier d'un intervalle réel JO - Annales de l'Institut Fourier PY - 1990 SP - 885 EP - 911 VL - 40 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1240/ DO - 10.5802/aif.1240 LA - fr ID - AIF_1990__40_4_885_0 ER -
Amoroso, Francesco. Sur le diamètre transfini entier d'un intervalle réel. Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 885-911. doi : 10.5802/aif.1240. http://www.numdam.org/articles/10.5802/aif.1240/
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