A new exceptional polynomial for the integer transfinite diameter of

Qiang Wu

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 3, page 847-861
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Wu, 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. [5] L. Habsieger, B. Salvy, On integer Chebyshev polynomials. Math. Comp.66 (1997), 763-770. Zbl0911.11033MR1401941
  6. [6] A.K. Lenstra, H.W. Lenstra, L. Lovasz, Factoring polynomials with rational coefficients. Math. Ann.261 (1982), 515-534. Zbl0488.12001MR682664
  7. [7] I.E. Pritsker, Small polynomials with integer coefficients. (submitted). Zbl1091.11009
  8. [8] Q. Wu, On the linear independence measure of logarithms of rational numbers. Math. Comp.72 (2003), 901-911. Zbl1099.11037MR1954974
  9. [9] Q. Wu, Mesure d'indépendance linéaire de logarithmes et diamètre transfini entier. Thèse, Univ. de Metz, 2000. 

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