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Trace formula and the distribution of eigenvalues of Schroedinger operators on manifolds all of whose geodesics are closed

机译：跟踪公式和schroedinger算子的特征值的分布在所有的测地线都关闭的流形上

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We investigate the behaviour of the remainder term R(E) in the Weyl formula (l brace)nvertical stroke E(sub n)(<=)E(r brace)=Vol(M).E(sup d/2)/((4(pi))(sup d/2)(Gamma)(d/2+1))+R(E) for the eigenvalues E(sub n) of a Schroedinger operator on a d-dimensional compact Riemannian manifold all of whose geodesics are closed. We show that R(E) is of the form E(sup (d-1)/2)(Theta)((radical)E), where (Theta)(x) is an almost periodic function of Besicovitch class B(sup 2) which has a limit distribution whose density is a box-shaped function. Furthermore we derive a trace formula and study higher order terms in the asymptotics of the coefficients related to the periodic orbits. The periodicity of the geodesic flow leads to a very simple structure of the trace formula which is the reason why the limit distribution can be computed explicitly. (orig.)

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