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Periods of Hecke Characters

  • Authors
  • NorbertĀ Schappacher

Part of the Lecture Notes in Mathematics book series (LNM, volume 1301)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Norbert Schappacher
    Pages 1-22
  3. Norbert Schappacher
    Pages 23-80
  4. Norbert Schappacher
    Pages 81-116
  5. Norbert Schappacher
    Pages 117-127
  6. Norbert Schappacher
    Pages 128-137
  7. Norbert Schappacher
    Pages 138-147
  8. Back Matter
    Pages 148-160

About this book

Introduction

The starting point of this Lecture Notes volume is Deligne's theorem about absolute Hodge cycles on abelian varieties. Its applications to the theory of motives with complex multiplication are systematically reviewed. In particular, algebraic relations between values of the gamma function, the so-called formula of Chowla and Selberg and its generalization and Shimura's monomial relations among periods of CM abelian varieties are all presented in a unified way, namely as the analytic reflections of arithmetic identities beetween Hecke characters, with gamma values corresponding to Jacobi sums. The last chapter contains a special case in which Deligne's theorem does not apply.

Keywords

Arithmetic Identity algebra function theorem

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0082094
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-18915-2
  • Online ISBN 978-3-540-38842-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site