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Mathematical Sciences Research Institute Publications : Heegner Points and Rankin L-Series Series Number 49 - Henri Darmon

Mathematical Sciences Research Institute Publications

Heegner Points and Rankin L-Series Series Number 49

By: Henri Darmon (Editor), Shou-Wu Zhang (Editor)

Hardcover

Published: 31st May 2016
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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.

"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

Preface
Heegner points: the beginnings
Correspondence
The Gauss class number problem for imaginary quadratic fields
Heegner points and representation theory
Special value formulae for Rankin L-functions
Gross-Zagier formula for GL(2), II
Special cycles and derivatives in Eisenstein series
Faltings' height and the Derivatives of Eisenstein series
Elliptic curves and analogies between number fields and function fields
Heegner points and elliptic curves of large rank over function fields
Periods and points attached to quadratic algebras
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521836593
ISBN-10: 052183659X
Series: Mathematical Sciences Research Institute Publications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 380
Published: 31st May 2016
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.3 x 16.1  x 2.6
Weight (kg): 0.71