On Fermat's equation over some quadratic imaginary number fields

DOI10.1007/s40993-018-0117-yzbMath1444.11050arXiv1710.10163OpenAlexW3104017640WikidataQ92915186 ScholiaQ92915186MaRDI QIDQ2316174

George C. Ţurcaş

Publication date: 26 July 2019

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

Full work available at URL: https://arxiv.org/abs/1710.10163

zbMATH Keywords

Fermat's last theoremmodularity of elliptic curvesmod-\(p\) modular formsSerre's conjecture on Galois representations

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Galois representations (11F80) Higher degree equations; Fermat's equation (11D41) Cohomology of arithmetic groups (11F75)

Related Items (7)

Asymptotic Fermat for signatures (p,p,2)$(p,p,2)$ and (p,p,3)$(p,p,3)$ over totally real fields ⋮ On the solutions of $x^p+y^p=2^rz^p$, $x^p+y^p=z^2$ over totally real fields ⋮ Asymptotic generalized Fermat’s last theorem over number fields ⋮ On Serre's modularity conjecture and Fermat's equation over quadratic imaginary fields of class number one ⋮ Class field theory, Diophantine analysis and the asymptotic Fermat's last theorem ⋮ Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields ⋮ On ternary Diophantine equations of signature(p,p,2)over number fields

Uses Software

• Magma
• LMFDB

Cites Work

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