Periods of Hecke Characters

1988
ISBN: 978-3-540-18915-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1301, 162 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Schappacher, Norbert

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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.