A new exceptional polynomial for the integer transfinite diameter of [0,1]
Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 847-861.

En améliorant l'algorithme utilisé par Habsieger et Salvy pour obtenir des polynômes à coefficients entiers de plus petite norme infinie sur [0, 1], nous étendons leur table de polynômes jusqu'au degré 100. Au degré 95 nous trouvons un nouveau polynôme exceptionnel qui a des racines complexes. Notre méthode fait appel à des polynômes de Müntz-Legendre généralisés. Nous améliorons un peu la majoration du diamètre transfini entier de [0,1] et nous donnons une démonstration élémentaire de la minoration des exposants de certains polynômes critiques.

Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials.

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     title = {A new exceptional polynomial for the integer transfinite diameter of $[0,1]$},
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Qiang Wu. A new exceptional polynomial for the integer transfinite diameter of $[0,1]$. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 847-861. doi : 10.5802/jtnb.430. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.430/

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