Quasinormal modes of charged scalars around dilaton black holes in 2+1 dimensions: Exact frequencies

We have studied the charged scalar perturbation around a dilaton black hole in 2+1 dimensions. The wave equations of a massless charged scalar field are shown to be exactly solvable in terms of hypergeometric functions. The quasinormal frequencies are computed exactly. The relation between the quasinormal frequencies and the charge of the black hole, charge of the scalar, and the temperature of the black hole are analyzed. The asymptotic form of the real part of the quasinormal frequencies is evaluated exactly.