English
On binary quartic Thue equations and related topics
Virtualconference
Auteurs : Walsh, Gary (Auteur de la Conférence)
CIRM (Editeur )
11D25 - Cubic and quartic equations
11D57 - Multiplicative and norm form equations
11R16 - Cubic and quartic extensions
CIRM (Editeur )
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Résumé :
In a recent paper, Istvan Gaal and Laszlo Remete studied the integer solutions to binary quartic Thue equations of the form $x^4-dy^4 = \pm 1$, and used their results to determine pure quartic number fields which contain a power integral basis. In our talk, we propose a new way to approach this diophantine problem, and we also show how an effective version of the abc conjecture would allow for even further improvements. This is joint work with M.A. Bennett. We also discuss a relation between this quartic diophantine equation to recent joint work with P.-Z. Yuan.
Keywords : index form; integral basis; quadric fields; elliptic curves
Codes MSC : Keywords : index form; integral basis; quadric fields; elliptic curves
11D25 - Cubic and quartic equations
11D57 - Multiplicative and norm form equations
11R16 - Cubic and quartic extensions
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 01/12/2020 Date de captation : 25/11/2020 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : MP4 (.mp4) - HD Durée : 00:51:02 Audience : Researchers Download : https://videos.cirm-math.fr/2020-11-25_Walsh.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoireOrganisateurs de la rencontre : Rivat, Joël ; Tichy, Robert Dates : 23/11/2020 - 27/11/2020 Année de la rencontre : 2020 URL Congrès : https://www.chairejeanmorlet.com/2256.html
Données de citation
DOI : 10.24350/CIRM.V.19689803Citer cette vidéo: Walsh, Gary (2020). On binary quartic Thue equations and related topics. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19689803 URI : http://dx.doi.org/10.24350/CIRM.V.19689803 |
Voir aussi
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Bibliographie
- GAÁL, István et REMETE, László. Binomial Thue equations and power integral bases in pure quartic fields. arXiv preprint arXiv:1810.00063, 2018. - https://arxiv.org/abs/1810.00063
- ZAGIER, Don. Large integral points on elliptic curves. Mathematics of Computation, 1987, vol. 48, no 177, p. 425-436. - http://dx.doi.org/10.1090/S0025-5718-1987-0866125-3
