Automorphic Green’s functions and regulators of elliptic curves – Jeanine van Order (PUC-Rio)

The refined conjecture of Birch and Swinnerton-Dyer predicts a relation between the regulator of an elliptic curve and the leading term in the Taylor series expansion around s=1 of its Hasse-Weil L-function. I will explain how such relations can be derived in the special case of rank one, including some new results for elliptic curves over abelian extensions of real quadratic fields.