Sur le diamètre transfini entier d'un intervalle réel
Annales de l'Institut Fourier, Volume 40 (1990) no. 4, p. 885-911

Some new upper and lower bound for the least deviation from zero of integral polynomials over intervals I 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 I and on the denominators of its extremities.

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 I d’extrémités rationnelles. Ces encadrements dépendent explicitement de la longueur de I et des dénominateurs de ses extrémités.

@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},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {40},
     number = {4},
     year = {1990},
     pages = {885-911},
     doi = {10.5802/aif.1240},
     mrnumber = {1096596},
     zbl = {0713.41004},
     mrnumber = {92j:11070},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1990__40_4_885_0}
}
Amoroso, Francesco. Sur le diamètre transfini entier d'un intervalle réel. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 885-911. doi : 10.5802/aif.1240. http://www.numdam.org/item/AIF_1990__40_4_885_0/

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