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We present Atacama Large Millimeter/submillimeter Array Band 6 (1.3 mm) observations of dense cores in three massive molecular clouds within the central molecular zone (CMZ) of the Milky Way, including the Dust Ridge cloud e, Sgr C, and the 20 km s⁻¹cloud, at a spatial resolution of 2000 au. Among the 834 cores identified from the 1.3 mm continuum, we constrain temperatures and linewidths of 253 cores using local thermodynamic equilibrium methods to fit the H₂CO and/or CH₃CN spectra. We determine their masses using the 1.3 mm dust continuum and derived temperatures, and then evaluate their virial parameters using the H₂CO and/or CH₃CN linewidths and construct the core mass functions (CMFs). We find that the contribution of external pressure is crucial for the virial equilibrium of the dense cores in the three clouds, which contrasts with the environment in the Galactic disk where dense cores are already bound, even without the contribution of external pressure. With our new temperature estimates we also find that the CMFs show a Salpeter-like slope in the high-mass (≳3–6M_⊙) end, a change from previous works. Combined with the possible top-heavy initial mass functions (IMFs) in the CMZ, our result suggests that gas accretion and further fragmentation may play important roles in transforming the CMF to the IMF.