  The origin of the stellar Initial Mass Function (IMF) and how it may vary
with galactic environment is a matter of debate. Certain star formation
theories involve a close connection between the IMF and the Core Mass Function
(CMF) and so it is important to measure this CMF in a range of locations in the
Milky Way. Here we study the CMF of three Galactic Center clouds: G0.253+0.016
("The Brick"), Sgr B2 (Deep South field) and Sgr C. We use ALMA 1 mm continuum
images and identify cores as peaks in thermal dust emission via the dendrogram
algorithm. We develop a completeness correction method via synthetic core
insertion, where a realistic mass-dependent size distribution is used for the
synthetic cores. After corrections, a power law of the form
$\text{d}N/\text{d}\log M \propto M^{-\alpha}$ is fit to the CMFs above 2
M$_\odot$. The three regions show disparate CMFs, with the Brick showing a
Salpeter-like power law index $\alpha=1.21\pm0.11$ and the other two regions
showing shallower indices ($\alpha=0.92\pm0.09$ for Sgr C and
$\alpha=0.66\pm0.05$ for Sgr B2-DS). Furthermore, we analyze the spatial
distribution and mass segregation of cores in each region. Sgr C and Sgr B2-DS
show signs of mass segregation, but the Brick does not. We compare our results
to several other CMFs from different Galactic regions derived with the same
methods. Finally, we discuss how these results may help define an evolutionary
sequence of star cluster formation and can be used to test star formation
theories.
