## 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

## Project information

Project financing: |
The first author was supported by an EPSRC Leadership Fellowship. |
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## 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 |
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Refereed: | Yes |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra) > Chair Mathematics II (Computer Algebra) - 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 |