Goro Shimura

(Author)

Abelian Varieties with Complex Multiplication and Modular Functions: (Pms-46)Hardcover, 28 December 1997

Abelian Varieties with Complex Multiplication and Modular Functions: (Pms-46)
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Part of Series
Princeton Mathematical
Part of Series
Princeton Mathematical Series
Print Length
232 pages
Language
English
Publisher
Princeton University Press
Date Published
28 Dec 1997
ISBN-10
0691016569
ISBN-13
9780691016566

Description

Reciprocity laws of various kinds play a central role in number theory. In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions. A similar theory can be developed for special values of elliptic or elliptic modular functions, and is called complex multiplication of such functions. In 1900, Hilbert proposed the generalization of these as the twelfth of his famous problems. In this book, Goro Shimura provides the most comprehensive generalizations of this type by stating several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. This subject is closely connected with the zeta function of an abelian variety, which is also covered as a main theme in the book. The third topic explored by Shimura is the various algebraic relations among the periods of abelian integrals.

Product Details

Author:
Goro Shimura
Book Format:
Hardcover
Country of Origin:
US
Date Published:
28 December 1997
Dimensions:
24 x 16 x 1.91 cm
ISBN-10:
0691016569
ISBN-13:
9780691016566
Language:
English
Location:
Princeton
Pages:
232
Weight:
512.56 gm

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