... Mathematics, 162 (2005), 1353–1376 Twisted Fermat curves over totally real fields By Adrian Diaconu and Ye Tian Introduction Let p be a prime number, F a totally real field such that [F (µp ) : F ... Actually, the field over Q generated by the Hecke eigenvalues attached to f is F0 = Q(µp )+ , and for the CM abelian variety Jδ , we TWISTED FERMAT CURVES OVER TOTALLY REAL FIELDS 1357 have L(s ... unramified outside S and order dividing r Furthermore, TWISTED FERMAT CURVES OVER TOTALLY REAL FIELDS 1371 if e is replaced by e with e /e a real ideal, then both Ce, e , ρ and η not change Proof...