  We analyze analytically the asymptotic regions of the quasinormal mode
frequency spectra with infinitely large overtone numbers for $D$-dimensional
Schwarzschild black holes in anti de Sitter spacetimes. In this limit, we
confirm the analytic results obtained previously in the literature using
different methods. In addition, we show that in certain spacetime dimensions
these techniques imply the existence of other regions of the asymptotic
quasinormal mode frequency spectrum which have not previously appeared in the
literature. For large black holes, some of these modes have a damping rate of
$1.2T_H$, where $T_H$ is the Hawking temperature. This is less than the damping
rate of the lowest overtone quasinormal mode calculated by other authors. It is
not completely clear whether these modes actually exist or are an artifact of
an unknown flaw in the analytic techniques being used. We discuss the
possibility of the existence of these modes and explore some of the
consequences. We also examine the possible connection between the asymptotic
quasinormal modes of Schwarzschild-anti de Sitter black holes and the quantum
level spacing of their horizon area spectrum.
