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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
DOI: https://doi.org/10.1090/S0025-5718-98-00923-5
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 [Enhancements On Off] (What's this?)

  • [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: https://doi.org/10.1090/S0025-5718-98-00923-5
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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