Herleitung der Chowla-Selberg-Formel aus Shimura'schen Periodenrelationen. (Derivation of the Chowla-Selberg-formula from Shimura's period relations)
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.
transcendental factors in the periods of an abelian variety
scientific article; zbMATH DE number 3931176