In the context of analytic dynamical systems it is possible to usezeta functions and determinants to give good numerical estimates onassociated values, such as: Hausdorff Dimension of Limit sets; Entropyand Lyapunov exponents of hyperbolic systems; variance, etc. We willdiscuss the 2 method, illustrating it with specific examples,concentrating on new rigorous bounds on the errors in theapproximation. This is joint work with Oliver Jenkinson.