Cyclic vectors in Korenblum type spaces

In this paper we use the technique of premeasures, introduced by Korenblum in the 1970-s, to give a characterization of cyclic functions in the Korenblum type spaces ${\mathcal{A}}_{\mathrm{\Lambda }}^{-\mathrm{\infty }}$. In particular, we give a positive answer to a conjecture by Deninger (arXiv:1111.6416).