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.
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by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
by William Stein - University of Washington
Topics in this book: Rings of integers of number fields; Unique factorization of ideals in Dedekind domains; Structure of the group of units of the ring of integers; Finiteness of the group of equivalence classes of ideals of the ring of integers...
by Steve Wright - arXiv
This is a series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required.
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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.