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Absolute CM-Periods

Hiroyuki Yoshida Kyoto University, Kyoto, Japan
Available Formats:
Hardcover ISBN: 978-0-8218-3453-4
Product Code: SURV/106
List Price: $98.00 MAA Member Price:$88.20
AMS Member Price: $78.40 Electronic ISBN: 978-1-4704-1333-0 Product Code: SURV/106.E List Price:$92.00
MAA Member Price: $82.80 AMS Member Price:$73.60
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List Price: $147.00 MAA Member Price:$132.30
AMS Member Price: $117.60 Click above image for expanded view Absolute CM-Periods Hiroyuki Yoshida Kyoto University, Kyoto, Japan Available Formats:  Hardcover ISBN: 978-0-8218-3453-4 Product Code: SURV/106  List Price:$98.00 MAA Member Price: $88.20 AMS Member Price:$78.40
 Electronic ISBN: 978-1-4704-1333-0 Product Code: SURV/106.E
 List Price: $92.00 MAA Member Price:$82.80 AMS Member Price: $73.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$147.00 MAA Member Price: $132.30 AMS Member Price:$117.60
• 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.

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

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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.

• Appendix I. Eisenstein series on $GL(2)$
• Appendix II. On higher derivatives of $L$-functions