Non-vanishing of class group L-functions for number fields with a small regulator

摘要

Let E/Q be a number field of degree n. We show that if Reg(E) >(n,epsilon) vertical bar Disc(E)vertical bar(-1/4-epsilon). The proof is an interplay between almost equidistribution of Eisenstein periods over the toral packet in PGL(n)(Z) PGL(n) (R) associated to the maximal order of E, and the escape of mass of the torus orbit associated to the trivial ideal class.