Abelian Varieties with Complex Multiplication and Modular Functions

(PMS-46)

af Goro Shimura

Reciprocity 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.