Herleitung der Chowla-Selberg-Formel aus Shimura'schen Periodenrelationen. (Derivation of the Chowla-Selberg-formula from Shimura's period relations)
type: Item
instance of: scholarly article
title: Herleitung der Chowla-Selberg-Formel aus Shimura'schen Periodenrelationen. (Derivation of the Chowla-Selberg-formula from Shimura's period relations)
zbMATH Open document ID: 0582.14017
DOI: 10.1007/BF01189982
author: Matthias Flach
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: An explicit formula for the transcendental factors in periods of an abelian variety over \({\bar {\mathbb{Q}}}\) with complex multiplication by an abelian number field is given in terms of values of the gamma function at rational arguments. This result is easily derived from a reformulation due to Anderson of period relations originally due to Shimura. The Chowla-Selberg formula comes out as an immediate corollary.
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14K22
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 11F27
zbMATH DE Number: 3931176
zbMATH Keywords: transcendental factors in the periods of an abelian variety
zbMATH Keywords: complex multiplication
zbMATH Keywords: gamma function at rational arguments
zbMATH Keywords: period relations
zbMATH Keywords: Chowla-Selberg formula
MaRDI profile type: Publication
cites work: Q3966275
cites work: On the periods of Abelian integrals and a formula of Chowla and Selberg. With an appendix by David E. Rohrlich
cites work: Automorphic forms and the periods of abelian varieties
description: scientific article; zbMATH DE number 3931176