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Diameters of complete sets of conjugate algebraic integers of small degree
Author(s):
Michel
Grandcolas.
Journal:
Math. Comp.
67
(1998),
821-831.
MSC (1991):
Primary 11Y40, 11R09
MathSciNet review:
1451322
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Abstract:
We give bounds for the coefficients of a polynomial as functions of the diameter of its roots, hence we obtain polynomials with minimal diameters and small degree
References:
- [1]
- M. Langevin, E. Reyssat, and G. Rhin: Diamètres transfinis et problème de Favard (Ann. Inst. Fourier Grenoble, 38, 1, (1988), 1-16). MR 90b:11103
- [2]
- M. Langevin: Solutions des problèmes de Favard (Ann. Inst. Fourier Grenoble, 38, 2, (1988), 1-10). MR 90b:11104
- [3]
- J. Favard: Sur les nombres algébriques (C.R.Acad.Sc. Paris, 186, 1928, 1181-1182).
- [4]
- R.M. Robinson: Algebraic equations with span less than 4 (Math. Comp 18 (1964), 547-559). MR 29:6624
- [5]
- C. W. Lloyd-Smith: PhD Thesis Adelaide 1980, Problems on the distribution of conjugates of algebraic numbers.
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Additional Information:
Michel
Grandcolas
Affiliation:
UFR MIM, Département de Mathématiques, URA CNRS 399, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
Email:
Grandcol@poncelet.univ-metz.fr
DOI:
10.1090/S0025-5718-98-00923-5
PII:
S 0025-5718(98)00923-5
Keywords:
Polynomial,
diameter,
conjugate algebraic integers
Received by editor(s):
March 10, 1996
Received by editor(s) in revised form:
October 25, 1996
Copyright of article:
Copyright
1998,
American Mathematical Society
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