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Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0
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Siksek, S. and Stoll, M.. (2012) Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0. Bulletin of the London Mathematical Society , Vol.44 (No.1). pp. 151-166. ISSN 0024-6093
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Official URL: http://dx.doi.org/10.1112/blms/bdr086
Abstract
Let C: y(2)=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=f(1) f(2) ... f(r). We shall define a 'Selmer set' corresponding to this factorization with the property that if it is empty, then C(Q)=empty set. 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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Bulletin of the London Mathematical Society |
| Publisher: | Oxford University Press |
| ISSN: | 0024-6093 |
| Date: | 2012 |
| Volume: | Vol.44 |
| Number: | No.1 |
| Number of Pages: | 16 |
| Page Range: | pp. 151-166 |
| Identification Number: | 10.1112/blms/bdr086 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | EPSRC |
| URI: | http://wrap.warwick.ac.uk/id/eprint/42163 |
Data sourced from Thomson Reuters' Web of Knowledge
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