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• W2014701474 endingPage "787" @default.
• W2014701474 startingPage "763" @default.
• W2014701474 abstract "We prove that the equation A4 + B2 = Cp has no solutions in coprime positive integers when p ≥ 211. The main step is to show that, for all sufficiently large primes p, every [inline-graphic xmlns:xlink=http://www.w3.org/1999/xlink xlink:href=02i /]-curve over an imaginary quadratic field K with a prime of potentially multiplicative reduction greater than 6 has a surjective mod p Galois representation. The bound on p depends on K and the degree of the isogeny between E and its Galois conjugate, but is independent of the choice of E. The proof of this theorem combines geometric arguments due to Mazur, Momose, Darmon, and Merel with an analytic estimate of the average special values of certain L-functions." @default.
• W2014701474 created "2016-06-24" @default.
• W2014701474 creator A5071941381 @default.
• W2014701474 date "2004-01-01" @default.
• W2014701474 modified "2023-10-18" @default.
• W2014701474 title "Galois representations attached to Q-curves and the generalized Fermat equation A 4 + B 2 = C p" @default.
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• W2014701474 doi "https://doi.org/10.1353/ajm.2004.0027" @default.
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