Heegner Points and Rankin L-series

Henri Darmon, Shou-Wu Zhang

344 pages, parution le 21/06/2004

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Résumé

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.

Contributors:
Bryan Birch, Benedict Gross, Dorian Goldfeld, Brian Conrad, Vinayak Vatsal, Shouwu Zhang, Stephen Kudla, Tonghai Yang, Henri Darmon, Adrian Lovita, Massimo Bertonlini, Peter Green

Sommaire

Introduction
Heegner points: the beginnings
Letters to Dick Gross
The Gauss class number problem for imaginary quadratic fields
Heegner points and representation theory
Gross-Zagier revisited
Special value formulae for Rankin L-functions
Gross-Zagier formula for GL(2)
Special cycles and derivatives in Eisenstein series
Derivatives of Eisenstein series and Faltings' height
Elliptic curves and analogies between number fields and function fields
Heegner points and elliptic curves of large rank over function fields
Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms
Periods and points attached to quadratic algebras.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Henri Darmon, Shou-Wu Zhang
Parution	21/06/2004
Nb. de pages	344
Format	16 x 24
Couverture	Relié
Poids	670g
Intérieur	Noir et Blanc
EAN13	9780521836593
ISBN13	978-0-521-83659-3