Modularity of elliptic curves over abelian totally real fields   unramified at 3, 5, and 7
  This version improves the old version entitled "On the modularity of elliptic curves with a residually irreducible representation".   Let $E$ be an elliptic curve over an abelian totally real field $K$ unramified at 3,5, and 7. We prove that $E$ is modular. 
Sho Yoshikawa
math.NT