Solving Fermat-type equations via modular ℚ-curves over polyquadratic fields

DOI10.1515/CRELLE.2009.064zbMath1250.11033arXivmath/0611663OpenAlexW2105483796MaRDI QIDQ3647065

Jorge Jiménez-Urroz, Luis V. Dieulefait

Publication date: 27 November 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611663

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Higher degree equations; Fermat's equation (11D41)

Related Items (12)

Generalized Fermat equations: A miscellany ⋮ ℚ-Curves, Hecke characters and some Diophantine equations ⋮ Asymptotic Fermat for signature \((4, 2, p)\) over number fields ⋮ On the equation x2 + dy6 = zp for square-free 1 ≤ d ≤ 20 ⋮ \(\mathbb{Q}\)-curves, Hecke characters, and some Diophantine equations. II ⋮ Klein forms and the generalized superelliptic equation ⋮ Modular forms with large coefficient fields via congruences ⋮ On the equations a²−2b⁶=c^p and a²−2=c^p ⋮ On the generalized Fermat equation $a^2+3b^6=c^n$ ⋮ On a class of Lebesgue-Ljunggren-Nagell type equations ⋮ On the sum of fourth powers in arithmetic progression ⋮ The Fermat-type equations $x^5 + y^5 = 2z^p$ or $3z^p$ solved through $\mathbb {Q}$-curves

Cites Work

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• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
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