Heegner points and Rankin L-series

Author(s)

• Darmon, Henri Rene
• Zhang, Shouwu
• Workshop on Special Values of 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, c2004

• : hbk

Note

Includes bibliographical references

"This volume, based on a workshop on Special Values of Rankin L-Series held at the MSRI in December 2001 ..." - cover verso

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.

by "Nielsen BookData"

Details

• NCID: BA69198565
• ISBN:
  • 052183659X
• LCCN: 2004045108
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xiii, 367 p.
• Size: 25 cm
• Classification:
  • LCC : QA567.2.E44
• Subject Headings:
  • LCSH : Curves, Elliptic
  • LCSH : L-functions
• Parent Bibliography ID:
  • BA00044859