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9780521836593

Heegner Points and Rankin L-Series

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  • ISBN13:

    9780521836593

  • ISBN10:

    052183659X

  • Format: Hardcover
  • Copyright: 2004-06-21
  • Publisher: Cambridge University Press

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Summary

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.

Table of Contents

Preface ix
HENRI DARMON AND SHOU-WU ZHANG
Heegner Points: The Beginnings 1(10)
BRYAN BIRCH
Correspondence 11(14)
BRYAN BIRCH AND BENEDICT GROSS
The Gauss Class Number Problem for Imaginary Quadratic Fields 25(12)
DORIAN GOLDFELD
Heegner Points and Representation Theory 37(30)
BENEDICT GROSS
Gross-Zagier Revisited 67(98)
BRIAN CONRAD (with an appendix by W. R. MANN)
Special Value Formulae for Rankin L-Functions 165(26)
VINAYAK VATSAL
Gross-Zagier Formula for GL(2), II 191(52)
SHOU-WU ZHANG
Special Cycles and Derivatives of Eisenstein Series 243(28)
STEPHEN KUDLA
Faltings' Height and the Derivatives of Eisenstein Series 271(14)
TONGHAI YANG
Elliptic Curves and Analogies Between Number Fields and Function Fields 285(32)
DOUG ULMER
Heegner Points and Elliptic Curves of Large Rank over Function Fields 317(6)
HENRI DARMON
Periods and Points Attached to Quadratic Algebras 323
MASSIMO BERTOLINI, HENRI DARMON AND PETER GREEN

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