Bleher P.
Trace Formula for Quantum Integrable Systems, Lattice-Point Problem,
and Small Divisors
(68K, TeX)

ABSTRACT.  We review  rigorous results concerning almost periodicity by 
Besicovitch of the spectral function of quantum integrable systems,
lattice point-problem in convex and nonconvex domains, 
trace formula, and a related problem of small divisors. This includes 
the following subjects:
(i) Semiclassical quantization by Einstein-Brillouin-Keller and the
problem of completeness of semiclassical eigenfunctions.
(ii) The lattice-point problem.
(iii) The Gutzwiller-Berry-Tabor trace formula for quantum integrable
systems.
(iv) The problem of small divisors.
(v) The saturation phenomenon.