Verification of the Hamilton flow conditions associated with Weyl's conjecture

Anosov, D. V.: The geodesic flow on closed Riemannian manifolds of negative curvature. Proc. Steklov Inst. Math.90 (1967), 1–210 (Russian).Google Scholar

Arnold, V. I.: Mathematical methods of classical mechanics. Nauka, Moskow (1979) (Russian).Google Scholar

Berard, P. H.: On the wave equation on a compact Riemannian manifold without conjugate points. Math. Z.155 (1977), 249–276.Google Scholar

Bowen, R.: Periodic orbits for hyperbolic flows. Amer. J. Math.94 (1972), 1–30.Google Scholar

Chevalley, C.: Theory of Lie groups. Princeton Univ. Press, Princeton, New Jersey, 1946.Google Scholar

Duistermaat, J. J.; Guillemin, V. W.: The spectrum of positive elliptic operators and periodic bicharacteristics. Invent. Math29 (1975), 39–79.Google Scholar

Ivrii, V. J.: Precise spectral asymptotics for elliptic operators. Lecture Notes in Math., Springer 1984.Google Scholar

Vasiljev, D. G.: The asymptotics of the spectrum of boundary value problems. Trans. Moscow Math. Soc.49 (1986), 167–237 (Russian).Google Scholar

Volovoy, A. V.: The improvement of the remainder estimate in the two-term asymptotics of the eigenvalue distribution function of an elliptic operator on a compact manifold. Uspekhi Mat. Nauk 41 (1986) 4, 1985 (Russian).Google Scholar

Volovoy, A. V.: On the behaviour of the solution of the Cauchy problem on a compact manifold whent → + ∞. Uspekhi. Math. Nauk42 (1987) 2, 215–216 (Russian).Google Scholar

Volovoy, A. V.: The improved two-term asymptotics of the eigenvalue distribution function of an elliptic operator distribution function of an elliptic operator on a compact manifold. Dokl. Akad. Nauk SSSR294 (1987), 1037–1040 (Russian).Google Scholar

Randoll, B.: The Riemann hypothesis for Selberg's zeta-functions and the asymptotic behaviour of eigenvalues of the Laplace operator. Trans. Amer. Math. Soc.276 (1976), 203–223.Google Scholar