Abstract: The paper contains an investigation on basic problems
about the zeros of analytic theta functions. A brief introduction to
analytic representation of finite quantum systems is given. The zeros
of this function and there evolution time are discussed. Two open
problems are introduced. The first problem discusses the cases when
the zeros follow the same path. As the basis change the quantum state
|f transforms into different quantum state. The second problem is
to define a map between two toruses where the domain and the range
of this map are the analytic functions on toruses.