On a quantization of Jacobi's theta-functions

Jacobi's theta-functions and their theta-constants admit the redefinition through certain differential equations (dynamical systems); not through the canonical theta-series. We study these systems in the framework of Hamiltonian mechanics. Hamiltonians and Poisson structures have been found. All this prompts to formulate a quantization problem for the equations and gives rise some important problems. For a certain nontrivial case the problem is completely solvable up to a representation of operators and Hamiltonian spectrum.