Heegner Points and Rankin L-Series (Mathematical Sciences Research Institute Publications)
Cambridge University Press, 7/15/2010
EAN 9780521158206, ISBN10: 0521158206
Paperback, 382 pages, 23.4 x 15.6 x 2 cm
Language: English
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.
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.