Heegner points and Rankin L-series

Includes bibliography (365-367) and references.

1. Introduction 2. Heegner points: the beginnings 3. Letters to Dick Gross 4. The Gauss class number problem for imaginary quadratic fields 5. Heegner points and representation theory 6. Gross-Zagier revisited 7 Special value formulae for Rankin L-functions 8. Gross-Zagier formula for GL(2) 9. Special cycles and derivatives in Eisenstein series 10. Derivatives of Eisenstein series and Faltings' height 11. Elliptic curves and analogies between number fields and function fields 12. Heegner points and elliptic curves of large rank over function fields 13. Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms 14. Periods and points attached to quadratic algebras.

The seminal formula of Gross and Zagier relating heights of Heegner points to derivatives of the associated Rankin L-series has led to many generalisations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. This volume, based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, is a collection of thirteen articles written by many of the leading contributors in the field, having the Gross-Zagier formula and its avatars as a common unifying theme. It serves as a valuable reference for mathematicians wishing to become further acquainted with the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, Iwasawa theory, and other topics related to the Gross-Zagier formula.