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9780521158206

Heegner Points and Rankin L-Series

by
  • ISBN13:

    9780521158206

  • ISBN10:

    0521158206

  • Format: Paperback
  • Copyright: 2010-08-19
  • 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
Heegner points: the beginnings
Correspondence
The Gauss class number problem for imaginary quadratic fields
Heegner points and representation theory Brian Conrad (with an appendix by
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.

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