Heegner Points and Rankin L-Series

This collection of articles explores the Gross-Zagier formula's history and its implications in complex multiplication and L-series, as presented in Heegner Points and Rankin L-Series.

This volume, titled Heegner Points and Rankin L-Series, presents a collection of thirteen insightful articles contributed by prominent figures in the field. The articles delve into the rich history and ongoing developments related to the Gross-Zagier formula, which establishes a significant connection between the heights of Heegner points and the derivatives of associated Rankin L-series. This foundational formula has catalyzed numerous generalizations and extensions, creating a vibrant area of mathematical inquiry that continues to evolve.

The topics explored in this collection include complex multiplication theory, automorphic forms, the Rankin-Selberg method, and arithmetic intersection theory, among others. Each article reflects the contributions of leading scholars, offering a comprehensive overview of the advancements that have emerged from the Gross-Zagier formula. This makes the volume a valuable resource for mathematicians seeking to deepen their understanding of these interconnected subjects.

Based on a workshop held at the MSRI in December 2001, Heegner Points and Rankin L-Series serves not only as a historical account but also as a guide for current and future research. The unifying theme of the Gross-Zagier formula throughout these articles highlights its significance in the mathematical community, making this collection essential for those interested in the ongoing dialogue surrounding these complex topics.