Evaluation of Spectral Zeta-Functions with the Renormalization Group

We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal-Kadanoff bond moving scheme from regular lattices. As possible applications of these results we mention quantum search algorithms as well as synchronization, which we discuss in more detail.