A REFINED MODULAR APPROACH TO THE DIOPHANTINE EQUATION x2 + y2n = z3
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Publication:3173270
DOI10.1142/S1793042111004472zbMath1226.11043arXiv1002.0020OpenAlexW2964118337MaRDI QIDQ3173270
Publication date: 27 September 2011
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1002.0020
Elliptic curves over global fields (11G05) Holomorphic modular forms of integral weight (11F11) Galois representations (11F80) Higher degree equations; Fermat's equation (11D41)
Related Items (5)
Generalized Fermat equations: A miscellany ⋮ On some generalized Fermat equations of the form x2+y2n=zp$x^2+y^{2n} = z^p$ ⋮ A multi-Frey approach to Fermat equations of signature $(r,r,p)$ ⋮ On a class of generalized Fermat equations of signature \((2,2n,3)\) ⋮ On a class of Lebesgue-Ljunggren-Nagell type equations
Cites Work
- Unnamed Item
- On Néron's classification of elliptic curves of residue characteristics 2 and 3
- Perfect powers expressible as sums of two cubes
- Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\)
- Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
- On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
- Modular elliptic curves and Fermat's Last Theorem
- Ring-theoretic properties of certain Hecke algebras
- The Diophantine equation \(Ax^ p+By^ q=Cz^ r\).
- The primitive solutions to \(x^3+y^9=z^2\)
- On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
- Sur l'équation a3+ b3= cp
- Ternary Diophantine Equations via Galois Representations and Modular Forms
- On the Equations zm = F (x, y ) and Axp + Byq = Czr
- On the equation $s^2+y^{2p} = \alpha^3$
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