Modular elliptic curves over real abelian fields and the generalized Fermat equation \(x^{2\ell}+y^{2m}=z^p\)

DOI10.2140/ant.2016.10.1147zbMath1419.11056arXiv1506.02860OpenAlexW1204290162MaRDI QIDQ313940

Samuele Anni, Samir Siksek

Publication date: 12 September 2016

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.02860

zbMATH Keywords

elliptic curvesGalois representationHilbert modular formsirreducibilitymodularityFermat-Catalangeneralized Fermatlevel lowering

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80) Higher degree equations; Fermat's equation (11D41) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (5)

On elliptic curves with p-isogenies over quadratic fields ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ Some extensions of the modular method and Fermat equations of signature \((13,13,n)\) ⋮ Fermat's theorem over some totally real number fields ⋮ Points of order 13 on elliptic curves

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