Modular elliptic curves over real abelian fields and the generalized Fermat equation x(2l) + y(2m) = z(p)

摘要

Let K be a real abelian field of odd class number in which 5 is unramified. Let S-5 be the set of places of K above 5. Suppose for every nonempty proper subset S subset of S-5 there is a totally positive unit u is an element of O-K such that