Numerical computations

Abstract

Because resonances are defined by meromorphic continuation, direct computation via the resolvent is very difficult. The product definition (2.23) of the Selberg zeta function has the same difficulty; the formula does not apply in the region of interest. However, for hyperbolic surfaces without cusps, the dynamical zeta function introduced in §15.3 provides a suitable alternative. The transfer operator is trace-class for any value of s ϵ ℂ, so analytic continuation is not required.