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.
General
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