Heegner Points and Rankin L-Series
Heegner Points and Rankin L-Series
Shou-wu Zhang, Columbia University, New York
Mathematical Sciences Research Institute
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.
- Includes historical and expository articles by some of the leading contributors in the field
- Valuable reference for mathematicians
- Based on a workshop on Special Values of Rankin L-series
Product details
August 2010Paperback
9780521158206
382 pages
229 × 152 × 20 mm
0.51kg
Available
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.
