Thue equations with composite fields
Identifieur interne : 006538 ( Hal/Checkpoint ); précédent : 006537; suivant : 006539Thue equations with composite fields
Auteurs : Yuri Bilu [France, Suisse] ; Guillaume Hanrot [France]Source :
Descripteurs français
Abstract
We consider the Thue equation $F(x,y)=a$, where $F$ is an irreducible form of degree $n\geq 3$.We describe a method of resolution which takes advantage of the fact that the number field generated by a root of $F(1,y)$ has small subfields. We illustrate this method by solving several real cyclotomic equations of degrees as large as 2505. || Considérons l'équation de Thue $F(x,y)=a$, avec $F$ une forme irréductible homogène de degré $n\geq 3$. Nous décrivons une méthode de résolution permettant de tirer profit de l'existence de petits sous-corps du corps de nombres engendré par une racine
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<abstract xml:lang="en">We consider the Thue equation $F(x,y)=a$, where $F$ is an irreducible form of degree $n\geq 3$.We describe a method of resolution which takes advantage of the fact that the number field generated by a root of $F(1,y)$ has small subfields. We illustrate this method by solving several real cyclotomic equations of degrees as large as 2505. || Considérons l'équation de Thue $F(x,y)=a$, avec $F$ une forme irréductible homogène de degré $n\geq 3$. Nous décrivons une méthode de résolution permettant de tirer profit de l'existence de petits sous-corps du corps de nombres engendré par une racine</abstract>
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