Periods of Hecke Characters

Norbert Schappacher (auth.)9780387189154, 0-387-18915-7, 3540189157

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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Table of contents :
Algebraic hecke characters….Pages 1-22
Motives for algebraic hecke characters….Pages 23-80
The periods of algebraic hecke characters….Pages 81-116
Elliptic integrals and the gamma function….Pages 117-127
Abelian integrals with complex multiplication….Pages 128-137
Motives of CM modular forms….Pages 138-147