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The Padoan and Nordlund model of the stellar initial mass function (IMF) isderived from low order statistics of supersonic turbulence, neglecting gravity(e.g. gravitational fragmentation, accretion and merging). In this work thepredictions of that model are tested using the largest numerical experiments ofsupersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date(~1000^3 computational zones) and three different codes (Enzo, Zeus and theStagger Code). The model predicts a power law distribution for large masses,related to the turbulence energy power spectrum slope, and the shock jumpconditions. This power law mass distribution is confirmed by the numericalexperiments. The model also predicts a sharp difference between the HD and MHDregimes, which is recovered in the experiments as well, implying that themagnetic field, even below energy equipartition on the large scale, is acrucial component of the process of turbulent fragmentation. These resultssuggest that the stellar IMF of primordial stars may differ from that in laterepochs of star formation, due to differences in both gas temperature andmagnetic field strength. In particular, we find that the IMF of primordialstars born in turbulent clouds may be narrowly peaked around a mass of order 10solar masses, as long as the column density of such clouds is not much inexcess of 10^22 cm^-2.Comment: Accepted for Ap

Two Regimes of Turbulent Fragmentation and the Stellar Initial Mass Function from Primordial to Present‐Day Star Formation