On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$

DOI10.1112/mtk.12127arXiv2107.03908MaRDI QIDQ6048786

Philippe Michaud-Jacobs

Publication date: 15 September 2023

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.03908

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)

Cites Work

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• Criteria for irreducibility of mod \(p\) representations of Frey curves
• Modular elliptic curves over real abelian fields and the generalized Fermat equation \(x^{2\ell}+y^{2m}=z^p\)
• Multi-Frey \(\mathbb Q\)-curves and the Diophantine equation \(a^2+b^6=c^n\)
• The Magma algebra system. I: The user language
• Modular elliptic curves and Fermat's Last Theorem
• Elliptic curves over totally real cubic fields are modular
• Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)
• The Generalized Fermat Equation
• Generalized Fermat equations: A miscellany
• The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• A REFINED MODULAR APPROACH TO THE DIOPHANTINE EQUATION x² + y²ⁿ = z³
• Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields
• THE DIOPHANTINE EQUATION A⁴ + 2^δB² = Cⁿ
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Chabauty Without the Mordell-Weil Group
• Fermat’s Last Theorem and modular curves over real quadratic fields

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