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.

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Bibliographic Information

Book Title: Periods of Hecke Characters
Authors: Norbert Schappacher
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0082094
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1988
Softcover ISBN: 978-3-540-18915-2Published: 24 February 1988
eBook ISBN: 978-3-540-38842-5Published: 14 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 162
Topics: Number Theory

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Table of contents (6 chapters)

Front Matter

Algebraic hecke characters

Motives for algebraic hecke characters

The periods of algebraic hecke characters

Elliptic integrals and the gamma function

Abelian integrals with complex multiplication

Motives of CM modular forms

Back Matter

About this book