TRACE FORMULAS FOR ARITHMETICAL SYSTEMS

For quantum problems on the pseudosphere generated by arithmetic group s there exist special trace formulas, called trace formulas for Hecke operators, which permit the reconstruction of wave. functions from the knowledge of periodic orbits. After a short discussion of this subjec t we present the Hecke operators' trace formulas for the Dirichlet pro blem on the modular billiard; which is a prototype of arithmetical sys tems. The results of numerical computations for these semiclassical-ty pe relations are in good agreement with the directly computed eigenfun ctions.