Zero sets of holomorphic functions in the Nevanlinna type class on convex domains in C2

We study a problem concerning zero sets of holomorphic functions in the Nevanlinna type class on convex domains (not necessarily finite type) in C2. We give a Blaschke type condition for the zero set defined by a function in the Nevanlinna type class on convex domains in C2. Moreover, we present an example of a convex domain of exponentially-flat infinite type on which it is possible to give sufficient conditions for zero sets of holomorphic functions in the classical Nevanlinna class.