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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.

Curves, Elliptic --- L-functions --- 512.75 --- Functions, L --- -Number theory --- Elliptic curves --- Curves, Algebraic --- 512.75 Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions --- Arithmetic problems of algebraic varieties. Rationality questions. Zeta-functions --- Curves, Elliptic. --- L-functions.