Quasinormal modes of scale dependent black holes in (1+2)-dimensional Einstein-power-Maxwell theory

We study for the first time the stability against scalar perturbations, and we compute the spectrum of quasinormal modes of three-dimensional charged black holes in Einstein-power-Maxwell non-linear electrodynamics assuming running couplings. Adopting the 6th order WKB approximation we investigate how the running of the couplings change the spectrum of the classical theory. Our results show that all modes corresponding to non-vanishing angular momentum are unstable both in the classical theory and with the running of the couplings, while the fundamental mode can be stable or unstable depending on the running parameter and the electric charge.