Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Collection Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

Organizer(s) Rivat, Joël ; Tichy, Robert

Date(s) 23/11/2020 - 27/11/2020

linked URL https://www.chairejeanmorlet.com/2256.html

00:00:00 / 00:00:00

2 28

On binary quartic Thue equations and related topics

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.

Information about the video

Date of recording 25/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19689803
Cite this video Walsh, Gary (25/11/2020). On binary quartic Thue equations and related topics. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19689803
URL https://dx.doi.org/10.24350/CIRM.V.19689803

Domain(s)

Number Theory

Bibliography

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

MSC codes

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