The Resource Abelian varieties with complex multiplication and modular functions, Goro Shimura

Abelian varieties with complex multiplication and modular functions, Goro Shimura

Label
Abelian varieties with complex multiplication and modular functions
Title
Abelian varieties with complex multiplication and modular functions
Statement of responsibility
Goro Shimura
Creator
Subject
Language
eng
Summary
  • 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
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1930-2019
http://library.link/vocab/creatorName
Shimura, Gorō
Illustrations
illustrations
Index
index present
LC call number
QA564
LC item number
.S458 1998
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Abelian varieties
  • Modular functions
  • Abelian varieties
  • Modular functions
  • Variëteiten van Abel
  • Modulaire functies
  • Variétés abéliennes
  • Fonctions modulaires
Label
Abelian varieties with complex multiplication and modular functions, Goro Shimura
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 209-214) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 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
  • Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)
  • Ch. I.
  • Preliminaries on Abelian Varieties
  • Ch. II.
  • Abelian Varieties with Complex Multiplication
  • Ch. III.
  • Reduction of Constant Fields
  • Ch. IV.
Dimensions
24 cm.
Extent
xiv, 217 pages
Isbn
9780691016566
Lccn
97008673
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)36713049
  • (OCoLC)ocm36713049
Label
Abelian varieties with complex multiplication and modular functions, Goro Shimura
Publication
Bibliography note
Includes bibliographical references (p. 209-214) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • 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
  • Preface to Complex Multiplication of Abelian Varieties and Its Applications to Number Theory (1961)
  • Ch. I.
  • Preliminaries on Abelian Varieties
  • Ch. II.
  • Abelian Varieties with Complex Multiplication
  • Ch. III.
  • Reduction of Constant Fields
  • Ch. IV.
Dimensions
24 cm.
Extent
xiv, 217 pages
Isbn
9780691016566
Lccn
97008673
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)36713049
  • (OCoLC)ocm36713049

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