Partial descent on hyperelliptic curves and the generalized Fermat equation x3+y4+z5=0
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 0024-6093Full text not available from this repository.
Official URL: http://dx.doi.org/10.1112/blms/bdr086
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|
|Number of Pages:||16|
|Page Range:||pp. 151-166|
|Access rights to Published version:||Restricted or Subscription Access|
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