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Partial descent on hyperelliptic curves and the generalized Fermat equation x³+y⁴+z⁵=0

Title data

Siksek, Samir ; Stoll, Michael:
Partial descent on hyperelliptic curves and the generalized Fermat equation x³+y⁴+z⁵=0.
In: The Bulletin of the London Mathematical Society. Vol. 44 (2012) Issue 1 . - pp. 151-166.
ISSN 0024-6093
DOI: https://doi.org/10.1112/blms/bdr086

Official URL: Volltext

Project information

Project financing: The first author was supported by an EPSRC Leadership Fellowship.

Abstract in another language

Let C: y²=f(x) be a hyperelliptic curve defined over ℚ. Let K be a number field and suppose f factors over K as a product of irreducible polynomials f=f₁ f₂ … fᵣ. We shall define a ‘Selmer set’ corresponding to this factorization with the property that if it is empty, then C(ℚ)=∅. We shall demonstrate the effectiveness of our new method by solving the generalized Fermat equation with signature (3, 4, 5), which is unassailable via the previously existing methods.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 28 Nov 2014 08:26
Last Modified: 28 Nov 2014 08:26
URI: https://eref.uni-bayreuth.de/id/eprint/4182