Diamètres transfinis et problème de Favard

Michel Langevin; E. Reyssat; Georges Rhin

Annales de l'institut Fourier (1988)

  • Volume: 38, Issue: 1, page 1-16
  • ISSN: 0373-0956

Abstract

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We show that each irrational algebraic integer has two conjugates whose distance is at least 3 . The proof uses lower bounds for discriminants of fields of small degree, elementary geometry and some machine computations.

How to cite

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Langevin, Michel, Reyssat, E., and Rhin, Georges. "Diamètres transfinis et problème de Favard." Annales de l'institut Fourier 38.1 (1988): 1-16. <http://eudml.org/doc/74791>.

@article{Langevin1988,
abstract = {Tout entier algébrique irrationnel a deux conjugués éloignés d’au moins $\sqrt\{3\}$.},
author = {Langevin, Michel, Reyssat, E., Rhin, Georges},
journal = {Annales de l'institut Fourier},
keywords = {Favard problem; conjugate algebraic integers},
language = {fre},
number = {1},
pages = {1-16},
publisher = {Association des Annales de l'Institut Fourier},
title = {Diamètres transfinis et problème de Favard},
url = {http://eudml.org/doc/74791},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Langevin, Michel
AU - Reyssat, E.
AU - Rhin, Georges
TI - Diamètres transfinis et problème de Favard
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 1
SP - 1
EP - 16
AB - Tout entier algébrique irrationnel a deux conjugués éloignés d’au moins $\sqrt{3}$.
LA - fre
KW - Favard problem; conjugate algebraic integers
UR - http://eudml.org/doc/74791
ER -

References

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  3. [Bl, LS, M] P.E. BLANKSBY, C.W. LLOYD-SMITH, M.J. MCAULEY, On diameters of algebraic integers, preprint à paraître. Zbl0693.12001
  4. [D] F. DIAZ Y DIAZ, Tables minorant la racine n-ième du discriminant d'un corps de degré n, Publications mathématiques d'Orsay, 1980. Zbl0482.12003
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  7. [L1] M. LANGEVIN, Approche géométrique du problème de Favard, CRAS, 10 (1987), 245-248. Zbl0608.12024MR88e:12001
  8. [L2] M. LANGEVIN, Etude géométrique de la mesure de Mahler et du diamètre transfini, preprint à paraître dans Pub. Math. Univ. St Etienne. 
  9. [LS1] C.W. LLOYD-SMITH, Problems on the distribution of conjugates of algebraic numbers, Ph. D. Thesis, Univ. of Adelaide, 1980. Zbl0474.12004
  10. [LS2] C.W. LLOYD-SMITH, On a problem of Favard concerning algebraic integers, Bull. Austral. Math. Soc., 29 (1984), 111-121. Zbl0545.12001MR85m:11065
  11. [M1] J. MARTINET, Petits discriminants des corps de nombres, in “Journées arithmétiques 1980”, J.V. Armitage éd., London Math. Soc. Lecture Notes Series, 56 (1982), 151-193. Zbl0491.12005MR84g:12009
  12. [M2] J. MARTINET, Méthodes géométriques dans la recherche des petits discriminants, Séminaire de théorie des nombres, Paris, 1983/1984, Birkhäuser. Zbl0567.12009
  13. [N] NEHARI, Conformal mapping, 1952. Zbl0048.31503MR13,640h
  14. [P] M. POHST, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields ; J. Number theory, 14 (1982), 99-117. Zbl0478.12005MR83g:12009

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