Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-28T10:39:47.301Z Has data issue: false hasContentIssue false

Weighted diameters of complete sets of conjugate algebraic integers

Published online by Cambridge University Press:  17 April 2009

Michel Grandcolas
Affiliation:
UFR MIM Département de Math´matiquesURA CRNS 399Université Metz, 57045 Metz Cédex 01France e-mail: grandcol@poncelet.univ-metz.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this work, we generalise the study of Favard's Problems to the weighted diameters of a complete set of conjugate algebraic integers, that is, the roots of an irreducible monic polynomial with coefficients in ℤ.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Langevin, M., Reyssat, E. and Rhin, G., ‘Diamètres transfinis et problèmes de Favard’, Ann. Inst. Fourier (Grenoble) 38 (1988), 116.Google Scholar
[2]Favard, J., ‘Sur les nombres algébriques’, C.R. Acad. Sci. Paris 186 (1928), 11811182.Google Scholar
[3]Lloy–Smith, C.W., Problems on the distribution of conjugates of algebraic numbers, (PhD Thesis) (The University of Adelaide, South Australia, 1980).Google Scholar
[4]Grandcolas, M., ‘Diameters of complete sets of conjugate algebraic integers of small degree’, Math. Comp. (to appear).Google Scholar
[5]Diaz, F. Diaz y, Tables minorant la racine nième du discriminant d'un corps de degré n (Publications Mathématiques d'Orsay, 1980).Google Scholar
[6]Martinet, J., ‘Méthodes géométriques dans la recherche de petits discriminants’, in Séminaire de théorie des nombres de Paris 1983–84 (Birkhäuser Boston, Boston, MA, 1985), pp. 147179.Google Scholar
[7]Langevin, M., ‘Solutions des problèmes de Favard’, Ann. Inst. Fourier (Grenoble) 38 (1988), 110.Google Scholar
[8]Robinson, R.M., ‘Algebraic equations with span less than 4’, Math. Comp. 18 (1964), 547559.CrossRefGoogle Scholar
[9]Fekete, M. and Szegö, G., ‘On algebraic equations with integral coefficients whose roots belong to a given point set’, Math. Z. (1955), 158172.CrossRefGoogle Scholar
[10]Mignotte, M., ‘Distance beetween the roots of a polynomial’, Appl. Algebra Eng. (1995), 327332.Google Scholar
[11]Rogers, C.A., ‘The product of n homogenous linear forms’, J. London Math. Soc. 24 (1949), 3139.CrossRefGoogle Scholar