Heegner Points and Rankin L-Series [Paperback]

Thirteen articles by leading contributors on the history of the Gross-Zagier formula and its developments.The original formula of Gross and Zagier has led to many generalizations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. Based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, this volume presents thirteen articles written by leading contributors on the history of the Gross-Zagier formula and recent developments. Topics include the theory of complex multipication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, and Iwasawa theory.The original formula of Gross and Zagier has led to many generalizations and extensions in a variety of different directions, spawning a fertile area of study that remains active to this day. Based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, this volume presents thirteen articles written by leading contributors on the history of the Gross-Zagier formula and recent developments. Topics include the theory of complex multipication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, and Iwasawa theory.Based on a workshop on Special Values of Rankin L-series held at the MSRI in December 2001, this volume presents thirteen articles written by leading contributors on the history of the Gross-Zagier formula and recent developments. Topics include the theory of complex multiplication, automorphic forms, the Rankin-Selberg method, arithmetic intersection theory, and Iwasawa theory.1. Preface Henri Darmon and Shour-Wu Zhang; 2. Heegner points: the beginnings Bryan Birch; 3. Correspondence Bryan Birch and Benedict Gross; 4. The Gauss class number problem for imaginary quadratic fields Dorian Goldfeld; 5. Heegner points and representation theory Brian Conrad (with an appendix by W. R. Mann); 6. Special value formulae for Rankin L-functions Vló