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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
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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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