A Characterization of Random Bloch Functions

In this paper, we introduce a necessary and sufficient condition on the complex sequence an4, Ý an 2 , so that Ý n 1 anzn represents a Bloch function for almost all choices of signs ‘‘ ,’’ answering a question left open by J. M. Anderson et al.Ž1974, J. Reine Agnew. Math. 270, 12 37..