Solving superelliptic diophantine equations by Baker's method
| dc.contributor.author | BILU, Yuri | |
| hal.structure.identifier | Polynomials, Combinatorics, Arithmetic [POLKA] | |
| dc.contributor.author | HANROT, Guillaume | |
| dc.date.issued | 1998 | |
| dc.identifier.issn | 0010-437X | |
| dc.description.abstractEn | We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms. The characteristic feature of our approach (as compared with the classical method is that we reduce the equation directly to the linear forms in logarithms, without intermediate use of Thue and linear unit equations. We show that the reduction method of Baker and Davenport is applicable for superelliptic equations, and develop a very efficient method for enumerating the solutions below the reduced bound. The method requires computing the algebraic data in number fields of degree pn(n-1)/2 at most; in many cases this number can be reduced. Two examples with p=3 and n=4 are given. | |
| dc.language.iso | en | |
| dc.publisher | Foundation Compositio Mathematica | |
| dc.subject | soution of diophantine equations | |
| dc.subject | méthode de Baker | |
| dc.subject | Baker's method | |
| dc.subject | résolution d'équations diophantiennes | |
| dc.title.en | Solving superelliptic diophantine equations by Baker's method | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1023/A:1000305028888 | |
| dc.subject.hal | Informatique [cs]/Autre [cs.OH] | |
| bordeaux.journal | Compositio Mathematica | |
| bordeaux.page | 273--312 | |
| bordeaux.volume | 112 | |
| bordeaux.issue | 3 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00098523 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00098523v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Compositio%20Mathematica&rft.date=1998&rft.volume=112&rft.issue=3&rft.spage=273--312&rft.epage=273--312&rft.eissn=0010-437X&rft.issn=0010-437X&rft.au=BILU,%20Yuri&HANROT,%20Guillaume&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||