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

Abelian Varieties with Complex Multiplication and Modular Functions : : (PMS-46) / / Goro Shimura.

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 funct...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
VerfasserIn:
Shimura, Goro,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1998
Year of Publication:2016
Language:English
Series:Princeton Mathematical Series
Online Access:
Physical Description:1 online resource (232 p.)
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Table of Contents:
  • Frontmatter
  • Contents
  • Preface
  • Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)
  • Notation and Terminology
  • I. Preliminaries on Abelian Varieties
  • II. Abelian Varieties with Complex Multiplication
  • III. Reduction of Constant Fields
  • IV. Construction of Class Fields
  • V. The Zeta Function of an Abelian Variety with Complex Multiplication
  • VI. Families of Abelian Varieties and Modular Functions
  • VII. Theta Functions and Periods on Abelian Varieties
  • Bibliography
  • Supplementary References
  • Index
  • About the Author

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