Heegner Points and Rankin L-Series
by Henri Darmon, Shou-Wu Zhang
Publisher: Cambridge University Press 2004
Number of pages: 382
This volume, based on a workshop on Special Values of Rankin L-Series held at the MSRI in December 2001, is a collection of 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 better 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.
Home page url
Download or read it online for free here:
(multiple PDF files)
by J.S. Milne
Contents: Preliminaries From Commutative Algebra; Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Valuations; Local Fields; Global Fields.
by Robert B. Ash - University of Illinois
Basic course in algebraic number theory. It covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer’s theorem, the factorization of prime ideals in Galois extensions, local and global fields, etc.
by F. Oggier - Nanyang Technological University
Contents: Algebraic numbers and algebraic integers (Rings of integers, Norms and Traces); Ideals (Factorization and fractional ideals, The Chinese Theorem); Ramification theory; Ideal class group and units; p-adic numbers; Valuations; p-adic fields.
by J. S. Milne
These are preliminary notes for a modern account of the theory of complex multiplication. The reader is expected to have a good knowledge of basic algebraic number theory, and basic algebraic geometry, including abelian varieties.