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Diameters of complete sets of conjugate
algebraic integers of small degree
Author:
Michel Grandcolas
Journal:
Math. Comp. 67 (1998), 821-831
MSC (1991):
Primary 11Y40, 11R09
MathSciNet review:
1451322
Full-text PDF Free Access
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Additional Information
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
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M.
Langevin, É.
Reyssat, and G.
Rhin, Diamètres transfinis et problème de
Favard, Ann. Inst. Fourier (Grenoble) 38 (1988),
no. 1, 1–16 (French, with English summary). MR 948997
(90b:11103)
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Michel
Langevin, Solution des problèmes de Favard, Ann. Inst.
Fourier (Grenoble) 38 (1988), no. 2, 1–10
(French, with English summary). MR 949008
(90b:11104)
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J. Favard: Sur les nombres algébriques (C.R.Acad.Sc. Paris, 186, 1928, 1181-1182).
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Raphael
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(29 #6624), http://dx.doi.org/10.1090/S0025-5718-1964-0169374-X
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C. W. Lloyd-Smith: PhD Thesis Adelaide 1980, Problems on the distribution of conjugates of algebraic numbers.
- [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:
http://dx.doi.org/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
Article copyright:
© Copyright 1998 American Mathematical Society
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