Random variables determined by the distributions of their digits in a numeration system with complex base - O., V. Shkol’nyi (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measure zero (C-type singular distribution) or is a rectangle (S-type singular distribution).