  The spectral problem of three-dimensional manifolds M_A admitting
Sol-geometry in Thurston's sense is investigated. Topologically M_A are torus
bundles over a circle with a unimodular hyperbolic gluing map A. The
eigenfunctions of the corresponding Laplace-Beltrami operators are described in
terms of the modified Mathieu functions. It is shown that the multiplicities of
the eigenvalues are the same for generic values of the parameters in the metric
and are directly related to the number of representations of an integer by a
given indefinite binary quadratic form. As a result the spectral statistics is
shown to disagree with the Berry-Tabor conjecture. The topological nature of
the monodromy for both classical and quantum systems on Sol-manifolds is
demonstrated.
