Hilbert modular forms, elliptic curves and the Hodge conjecture

D. Blasius

Abstract

A standard conjecture identifies the L-function of every Hilbert modular form of weight (2,...,2) with that of a suitable abelian variety. We show how this conjecture follows from the Hodge conjecture, and discuss other applications of the method, e.g. to proving unconditionally the Ramanujan conjecture for such forms.