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Problèmes D'effectivité sur les Quartiques de Fermat

Published online by Cambridge University Press:  17 April 2009

Élie Cali  and
Alain Kraus
Élie Cali
Affiliation:
App. 231, 9 rue de Sèvres, 92100 Boulogne, France, e-mail: elie.cali@wanadoo.fr
Alain Kraus
Affiliation:
Université Pierre et Marie Curie - Paris 6, Institut de Mathématiques, UMR 7586 du CNRS, 175 rue du Chevaleret, 75013 Paris, France, e-mail: kraus@math.jussieu.fr
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Let K be a number field. An element b ∈ K* being given, let Cb be the curve defined over K by the equation x4 + y4 = bz4. Let Cb(K) be the set of the K-rational points of Cb. This paper uses Dem'janenko and Manin type methods to obtain effective criteria for Cb(K) to be empty.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 1 , February 2007 , pp. 91 - 119
Copyright
Copyright © Australian Mathematical Society 2007

References

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