Heegner points and Rankin L-series

Bibliographic Information

Heegner points and Rankin L-series

edited by Henri Darmon, Shou-Wu Zhang

(Mathematical Sciences Research Institute publications, 49)

Cambridge University Press, 2010, c2004

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Includes bibliographical references

Description and Table of Contents

Description

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

  • 1. Preface Henri Darmon and Shour-Wu Zhang
  • 2. Heegner points: the beginnings Bryan Birch
  • 3. Correspondence Bryan Birch and Benedict Gross
  • 4. The Gauss class number problem for imaginary quadratic fields Dorian Goldfeld
  • 5. Heegner points and representation theory Brian Conrad (with an appendix by W. R. Mann)
  • 6. Special value formulae for Rankin L-functions Vinayak Vatsal
  • 7. Gross-Zagier formula for GL(2), II Shou-Wu Zhang
  • 8. Special cycles and derivatives in Eisenstein series Stephen Kudla
  • 9. Faltings' height and the Derivatives of Eisenstein series Tonghai Yang
  • 10. Elliptic curves and analogies between number fields and function fields Doug Ulmer
  • 11. Heegner points and elliptic curves of large rank over function fields Henri Darmon
  • 12. Periods and points attached to quadratic algebras Massimo Bertolini and Peter Green.

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Details

  • NCID
    BB03071254
  • ISBN
    • 9780521158206
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge
  • Pages/Volumes
    xiii, 367 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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