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Heegner Points and Rankin L-Series

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Overview

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.

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Editorial Reviews

From the Publisher
"The volume has an excellent array of topics and it is written by the leading mathematicians in the field. Each article serves well as an overview of the main concepts and definitely encourages the reader to pursue a deeper study of the field." MAA Reviews, Alvara Lozano-Robledo, Cornell University
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Product Details

Meet the Author

Henri Darmon is a professor at McGill University. He is the Director of Centre Interuniversitaire en Calcul Mathematique Alegrigue and the Editor-in-chief of the Canadian Journal of Mathematics. An active researcher, he has written numerous mathematical articles and monographs. He is also the recipient of several awards such as fellow of the Royal Society of Canada, the Ribenboim Prize of the Canadian Number Theory Association and the Carrie M. Deric Award for teaching.

Shou-Wu Zhang is a Professor of Mathematics at Columbia University. He has been Chair Professor at Tsinghua University and Chinese Academy of Sciences in Beijing, China. He has written articles for numerous mathematical journals, including Annals of Mathematics, Inventiones, and Journal of American Mathematics Society.

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Table of Contents

Preface
Heegner points : the beginnings 1
Correspondence 11
The Gauss class number problem for imaginary quadratic fields 25
Heegner points and representation theory 37
Gross-Zagier revisited
Appendix 67
Special value formulae for Rankin L-functions 165
Gross-Zagier formula for GL(2), II 191
Special cycles and derivatives of Eisenstein series 243
Faltings' height and the derivatives of Eisenstein series 271
Elliptic curves and analogies between number fields and function fields 285
Heegner points and elliptic curves of large rank over function fields 317
Periods and points attached to quadratic algebras 323
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