  The detection of radio pulsars within the central few parsecs of the Galaxy
would provide a unique probe of the gravitational and magneto-ionic
environments in the Galactic Center (GC) and, if close enough to Sgr A*,
precise tests of general relativity in the strong-field regime. While it is
difficult to find pulsars at radio wavelengths because of interstellar
scattering, the payoff from detailed timing of pulsars in the GC warrants a
concerted effort. To motivate pulsar surveys and help define search parameters
for them, we constrain the pulsar number and spatial distribution using a wide
range of multiwavelength measurements. These include the five known radio
pulsars within 15 arcmin of Sgr A*, radio and gamma-ray measurements of diffuse
emission, non-detections in high frequency pulsar surveys of the central
parsec, a catalog of radio point sources from an imaging survey, infrared
observations of massive star populations in the central few parsecs, candidate
pulsar wind nebulae in the inner 20 pc and estimates of the core-collapse
supernova rate based on X-ray measurements. We find that under current
observational constraints, the inner parsec of the Galaxy could harbor as many
as ~10^3 active radio pulsars that are beamed towards Earth. Such a large
population would distort the low-frequency measurements of both the intrinsic
spectrum of Sgr A* and the free-free absorption along the line of sight of Sgr
A*.
