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Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zetafunction $Z(s)$ for several disjoint strictly convex compact obstacles $K_i\subset \R^N, i = 1,..., \kappa_0,\: \ka_0 \geq 3,$ and let $R_{\chi}(z) = \chi(-\Delta_D - z^2)^{-1}\chi,\: \chi \in C_0^{\infty}(\R^N),$ be the cut-offresolvent of the Dirichlet Laplacian $-\Delta_D$ in $\Omega = \bar{\R^N\setminus \cup_{i = 1}^{k_0} K_i}$. We prove that there exists $\sigma_1 < s_0$such that $Z(s)$ is analytic for $\Re (s) \geq \sigma_1$ and the cut-offresolvent $R_{\chi}(z)$ has an analytic continuation for $\Im (z) < -\sigma_1,\: |\Re (z)| \geq C > 0.$

Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function