We prove an analogue of Selberg's trace formula for a delta potential on a hyperbolic surface of finite volume. For simplicity we restrict ourselves to surfaces with at most one cusp, but our methods can easily be extended to any number of cusps. In the case of a noncompact surface we derive perturbative analogues of Maass cusp forms, residual Maass forms and nonholomorphic Eisenstein series. The latter satisfy a functional equation as in the classical case. We also introduce a perturbative analogue of Selberg's zeta function and apply the trace formula to prove its meromorphic continuation to the complex plane as well as a functional equation.
Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
Determinant of Friederichs Dirichlet Laplacians on $2$-dimensional hyperbolic cones
我们用锥角和边界的测地半径明确地表示了二维双曲（高斯曲率-1）锥上Friederichs Dirichlet Laplacian的谱行列式.最近的论文“Riemann-Roch isometries in the non-compact orbifold setting，”J. Eur. Math.Soc.22（2020）由G. Freixas i Montplet和A.冯·皮皮奇的观点是不正确的
