The Fermat equation over \(\mathbb Q(\sqrt 2)\)

DOI10.1016/j.jnt.2004.06.006zbMath1078.11019OpenAlexW2041131782MaRDI QIDQ1764787

Paul Meekin, Frazer Jarvis

Publication date: 22 February 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.06.006

zbMATH Keywords

Hilbert modular formsmodularityFermat equation

Mathematics Subject Classification ID

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 (21)

FERMAT'S EQUATION OVER 2-BY-2 MATRICES ⋮ On the generalized Fermat equation over totally real fields ⋮ Équation de Fermat et nombres premiers inertes ⋮ Fermat-type equations of signature \((13,13,p)\) via Hilbert cuspforms ⋮ Generalized Fermat equations: A miscellany ⋮ Fermat’s Last Theorem and modular curves over real quadratic fields ⋮ The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields ⋮ On the solutions of $x^p+y^p=2^rz^p$, $x^p+y^p=z^2$ over totally real fields ⋮ COURBES ELLIPTIQUES SEMI-STABLES SUR LES CORPS DE NOMBRES ⋮ Torsion of elliptic curves over cubic fields ⋮ Fermat's theorem over some totally real number fields ⋮ The Fermat theorem over \(\mathbb Q(\sqrt{5})\) ⋮ On the modularity of supersingular elliptic curves over certain totally real number fields ⋮ On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one ⋮ Elliptic curves over real quadratic fields are modular ⋮ Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem ⋮ On Fermat's equation over some quadratic imaginary number fields ⋮ On asymptotic Fermat over the \(\mathbb{Z}_2\)-extension of \(\mathbb{Q}\) ⋮ Unnamed Item ⋮ SOLUTIONS OF THE CUBIC FERMAT EQUATION IN QUADRATIC FIELDS ⋮ Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\)

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Cites Work

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• Die Unmöglichkeit von \(x^ 6 + y^ 6 = z^ 6\) und \(x^ 9 + y^ 9 = z^ 9\) in quadratischen Körpern
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• Hilbert modular surfaces
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• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Die Fixpunkte einiger Hilbertscher Modulgruppen
• On the modularity of supersingular elliptic curves over certain totally real number fields
• Weitere Ergebnisse über \(x^ 3+y^ 3=z^ 3\) in quadratischen Körpern
• On the levels of mod l Hilbert modular forms
• Points of Low Degree on Smooth Plane Curves
• Algebraic points of low degree on the Fermat quintic
• The Diophantine equation $x^4 + y^4 = 1$ in algebraic number fields

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