Feustel, J. Representation of Picard modular forms by theta constants. (English) Zbl 0662.10020 Rev. Roum. Math. Pures Appl. 33, No. 4, 275-281 (1988). 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 Cited in 1 ReviewCited in 1 Document MSC: 11F27 Theta series; Weil representation; theta correspondences 32N10 Automorphic forms in several complex variables Keywords:graded rings of Picard modular forms; generators; theta constants Citations:Zbl 0384.32010; Zbl 0371.32024 PDFBibTeX XMLCite \textit{J. Feustel}, Rev. Roum. Math. Pures Appl. 33, No. 4, 275--281 (1988; Zbl 0662.10020)