Description
Book SynopsisReciprocity laws of various kinds play a central role in number theory. This book states several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. It also covers the zeta function of an abelian variety as a main theme.
Trade Review"[This book] is a beautifully written, self-contained and complete treatment of a subject of which G. Shimura is a founding master, and is a fundamental reference for any researcher or student of the antimetric theory of abelian varieties and modular functions, and in particular of its applications to class field theory."--Bulletin of the London Mathematical Society
Table of ContentsPreface Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961) Notation and Terminology Ch. I. Preliminaries on Abelian Varieties Ch. II. Abelian Varieties with Complex Multiplication Ch. III. Reduction of Constant Fields Ch. IV. Construction of Class Fields Ch. V. The Zeta Function of an Abelian Variety with Complex Multiplication Ch. VI. Families of Abelian Varieties and Modular Functions Ch. VII. Theta Functions and Periods on Abelian Varieties Bibliography Supplementary References Index
