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 Y. Kitaoka - Tata Institute of Fundamental Research
This book is concerned with the problem of representation of positive definite quadratic forms by other such forms. From the table of contents: Preface; Fourier Coefficients of Siegel Modular Forms; Arithmetic of Quadratic Forms.
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 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 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.