Cycles, L-functions and triple products of elliptic curves

A variant of a conjecture of Beilinson and Bloch relates the rank of the Griffiths group of a smooth projective variety over a number field to the order of vanishing of an L-function at the center of the critical strip. Presently, there is little evidence to support the conjecture, especially when the L-function vanishes to order greater than 1. We study 1-cycles on E3 for various elliptic curves E/ℚ. In each of the 76 cases considered we find that the empirical order of vanishing of the L-function is at least as large as our best lower bound on the rank of the Griffiths group. In 11 cases this lower bound is two.

Duke Scholars

Author Chadmark L. Schoen Mathematics