Abelian Varieties with Complex Multiplication and Modular Functions: (PMS-46)

Description

Provides comprehensive generalizations of complex multiplication and modular functions by stating several reciprocity laws in terms of abelian varieties, theta functions and modular functions of several variables, including Siegal modular functions. This subject is closely connected with the zeta function, which is also covered as a main theme of this book. The third topic explored is the various algebraic relations among the periods of abelian integrals.

Goro Shimura is Professor of Mathematics at Princeton University. He was awarded the Leroy P. Steele Prize in 1996 for lifetime achievement in mathematics by the American Mathematical Society. He is the author of Introduction to Arithmetic Theory of Automorphic Functions (Princeton).

"[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