  Pulsars orbiting the Galactic center black hole, Sgr A*, would be potential
probes of its mass, distance and spin, and may even be used to test general
relativity. Despite predictions of large populations of both ordinary and
millisecond pulsars in the Galactic center, none have been detected within 25
pc by deep radio surveys. One explanation has been that hyperstrong temporal
scattering prevents pulsar detections, but the recent discovery of radio
pulsations from a highly magnetized neutron star (magnetar) within 0.1 pc shows
that the temporal scattering is much weaker than predicted. We argue that an
intrinsic deficit in the ordinary pulsar population is the most likely reason
for the lack of detections to date: a "missing pulsar problem" in the Galactic
center. In contrast, we show that the discovery of a single magnetar implies
efficient magnetar formation in the region. If the massive stars in the central
parsec form magnetars rather than ordinary pulsars, their short lifetimes could
explain the missing pulsars. Efficient magnetar formation could be caused by
strongly magnetized progenitors, or could be further evidence of a top-heavy
initial mass function. Furthermore, current high-frequency surveys should
already be able to detect bright millisecond pulsars, given the measured degree
of temporal scattering.
