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 :
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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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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</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Thue equations with composite fields</title><author role="aut"><persName><forename type="first">Yuri</forename><surname>Bilu</surname></persName><email></email><idno type="idhal">yuri-bilu</idno><idno type="halauthor">139112</idno><orgName ref="#struct-364954"></orgName><affiliation ref="#struct-3630"></affiliation></author><author role="aut"><persName><forename type="first">Guillaume</forename><surname>Hanrot</surname></persName><email>Guillaume.Hanrot@loria.fr</email><idno type="halauthor">129657</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2343"></affiliation></author><editor role="depositor"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2006-10-19 15:40:29</date><date type="whenModified">2016-05-18 08:53:47</date><date type="whenReleased">2006-10-24 12:08:59</date><date type="whenProduced">1999</date></edition><respStmt><resp>contributor</resp><name key="108626"><persName><forename>Publications</forename><surname>Loria</surname></persName><email>publications@loria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00108051</idno><idno type="halUri">https://hal.inria.fr/inria-00108051</idno><idno type="halBibtex">bilu:inria-00108051</idno><idno type="halRefHtml">Acta Arithmetica, Instytut Matematyczny PAN, 1999, 88 (4), pp.311--326</idno><idno type="halRef">Acta Arithmetica, Instytut Matematyczny PAN, 1999, 88 (4), pp.311--326</idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="IMB">Institut de Mathématiques de Bordeaux</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno></seriesStmt><notesStmt><note type="commentary">Article dans revue scientifique avec comité de lecture.</note><note type="audience" n="1">Not set</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Thue equations with composite fields</title><author role="aut"><persName><forename type="first">Yuri</forename><surname>Bilu</surname></persName><idno type="idHal">yuri-bilu</idno><idno type="halAuthorId">139112</idno><orgName ref="#struct-364954"></orgName><affiliation ref="#struct-3630"></affiliation></author><author role="aut"><persName><forename type="first">Guillaume</forename><surname>Hanrot</surname></persName><email>Guillaume.Hanrot@loria.fr</email><idno type="halAuthorId">129657</idno><orgName ref="#struct-300009"></orgName><affiliation ref="#struct-2343"></affiliation></author></analytic><monogr><idno type="localRef">99-R-192 || bilu99b</idno><idno type="halJournalId" status="VALID">22884</idno><title level="j">Acta Arithmetica</title><imprint><publisher>Instytut Matematyczny PAN</publisher><biblScope unit="volume">88</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="pp">311--326</biblScope><date type="datePub">1999</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="fr">Equations de Thue</term><term xml:lang="fr">diophantine equations</term><term xml:lang="fr">Thue equations</term><term xml:lang="fr">équations diophantiennes</term></keywords><classCode scheme="halDomain" n="info.info-oh">Computer Science [cs]/Other [cs.OH]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><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></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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