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Absolute CM-Periods
 
Hiroyuki Yoshida Kyoto University, Kyoto, Japan
Absolute CM-Periods
Absolute CM-Periods
Hardcover ISBN:  978-0-8218-3453-4
Product Code:  SURV/106
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1333-0
Product Code:  SURV/106.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-3453-4
eBook: ISBN:  978-1-4704-1333-0
Product Code:  SURV/106.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Absolute CM-Periods
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Absolute CM-Periods
Absolute CM-Periods
Hiroyuki Yoshida Kyoto University, Kyoto, Japan
Hardcover ISBN:  978-0-8218-3453-4
Product Code:  SURV/106
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1333-0
Product Code:  SURV/106.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-3453-4
eBook ISBN:  978-1-4704-1333-0
Product Code:  SURV/106.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 1062003; 282 pp
    MSC: Primary 11; 33; Secondary 30;

    The central theme of this book is an invariant attached to an ideal class of a totally real algebraic number field. This invariant provides us with a unified understanding of periods of abelian varieties with complex multiplication and the Stark-Shintani units. This is a new point of view, and the book contains many new results related to it.

    To place these results in proper perspective and to supply tools to attack unsolved problems, the author gives systematic expositions of fundamental topics. Thus the book treats the multiple gamma function, the Stark conjecture, Shimura's period symbol, the absolute period symbol, Eisenstein series on \(GL(2)\), and a limit formula of Kronecker's type. The discussion of each of these topics is enhanced by many examples. The majority of the text is written assuming some familiarity with algebraic number theory. About thirty problems are included, some of which are quite challenging.

    The book is intended for graduate students and researchers working in number theory and automorphic forms.

    Readership

    Graduate students and research mathematicians interested in number theory and algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • I. Multiple gamma function and its generalizations
    • II. The Stark–Shintani conjecture
    • III. Absolute CM–periods
    • IV. Explicit cone decompositions and applications
    • V. Applications of a limit formula of Kronecker’s type
    • Appendix I. Eisenstein series on $GL(2)$
    • Appendix II. On higher derivatives of $L$-functions
    • Appendix III. Transcendental property of CM-periods
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1062003; 282 pp
MSC: Primary 11; 33; Secondary 30;

The central theme of this book is an invariant attached to an ideal class of a totally real algebraic number field. This invariant provides us with a unified understanding of periods of abelian varieties with complex multiplication and the Stark-Shintani units. This is a new point of view, and the book contains many new results related to it.

To place these results in proper perspective and to supply tools to attack unsolved problems, the author gives systematic expositions of fundamental topics. Thus the book treats the multiple gamma function, the Stark conjecture, Shimura's period symbol, the absolute period symbol, Eisenstein series on \(GL(2)\), and a limit formula of Kronecker's type. The discussion of each of these topics is enhanced by many examples. The majority of the text is written assuming some familiarity with algebraic number theory. About thirty problems are included, some of which are quite challenging.

The book is intended for graduate students and researchers working in number theory and automorphic forms.

Readership

Graduate students and research mathematicians interested in number theory and algebraic geometry.

  • Chapters
  • I. Multiple gamma function and its generalizations
  • II. The Stark–Shintani conjecture
  • III. Absolute CM–periods
  • IV. Explicit cone decompositions and applications
  • V. Applications of a limit formula of Kronecker’s type
  • Appendix I. Eisenstein series on $GL(2)$
  • Appendix II. On higher derivatives of $L$-functions
  • Appendix III. Transcendental property of CM-periods
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.