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Representation of Picard modular forms by theta constants. (English) Zbl 0662.10020

The author describes his investigations of graded rings of Picard modular forms for the field \({\mathbb{Q}}(\sqrt{-3})\). The case \({\mathbb{Q}}(\sqrt{-1})\) was treated earlier by H. L. Resnikoff and Y. S. Tai [Math. Ann. 238, 97-117 (1978; Zbl 0371.32024)]. The main result is the explicit description of certain graded rings of Picard modular forms for \({\mathbb{Q}}(\sqrt{-3})\). The generators are given in terms of theta constants. For details the author refers to his preprint “Ringe automorpher Formen auf der komplexen Einheitskugel und ihrer Erzeugung durch Theta-Konstanten”, Karl-Weierstrass-Institut für Mathematik, Berlin 1985.
Reviewer: S.Böcherer

MSC:

11F27 Theta series; Weil representation; theta correspondences
32N10 Automorphic forms in several complex variables
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