A new exceptional polynomial for the integer transfinite diameter of
Journal de théorie des nombres de Bordeaux (2003)
- Volume: 15, Issue: 3, page 847-861
- ISSN: 1246-7405
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topWu, Qiang. "A new exceptional polynomial for the integer transfinite diameter of $[0,1]$." Journal de théorie des nombres de Bordeaux 15.3 (2003): 847-861. <http://eudml.org/doc/249099>.
@article{Wu2003,
abstract = {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.},
author = {Wu, Qiang},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {integer Chebyshev polynomials; transfinite diameter},
language = {eng},
number = {3},
pages = {847-861},
publisher = {Université Bordeaux I},
title = {A new exceptional polynomial for the integer transfinite diameter of $[0,1]$},
url = {http://eudml.org/doc/249099},
volume = {15},
year = {2003},
}
TY - JOUR
AU - Wu, Qiang
TI - A new exceptional polynomial for the integer transfinite diameter of $[0,1]$
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 847
EP - 861
AB - 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.
LA - eng
KW - integer Chebyshev polynomials; transfinite diameter
UR - http://eudml.org/doc/249099
ER -
References
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- [5] L. Habsieger, B. Salvy, On integer Chebyshev polynomials. Math. Comp.66 (1997), 763-770. Zbl0911.11033MR1401941
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- [9] Q. Wu, Mesure d'indépendance linéaire de logarithmes et diamètre transfini entier. Thèse, Univ. de Metz, 2000.
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