Absolute CM-Periods (Mathematical Surveys and Monographs Series)

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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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 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 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 illustrative examples. The major part of the text is written assuming, in addition to basic knowledge, some familiarity with algebraic number theory. About thirty problems are included for exercises, some of which are quite challenging. The book is intended for graduate students and researchers working in number theory and automorphic forms.

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Product Details

Table of Contents

Preface
Notation and Terminology
Introduction 1
Ch. I Multiple Gamma Function and Its Generalizations 13
Ch. II The Stark-Shintani Conjecture 43
Ch. III Absolute CM-Periods 61
Ch. IV Explicit Cone Decompositions and Applications 135
Ch. V Applications of a Limit Formula of Kronecker's Type 169
App. I Eisenstein Series on GL(2) 215
App. II On Higher Derivatives of L-Functions 249
App. III Transcendental Property of CM-Periods 269
References 275
Index 281
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