  We define a dynamical residue which generalizes the Guillemin-Wodzicki
residue density of pseudo-differential operators. More precisely, given a
Schwartz kernel, the definition refers to Pollicott-Ruelle resonances for the
dynamics of scaling towards the diagonal. We apply this formalism to complex
powers of the wave operator and we prove that residues of Lorentzian spectral
zeta functions are dynamical residues. The residues are shown to have local
geometric content as expected from formal analogies with the Riemannian case.
