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abstract: 'We report results from numerical simulations of star formation in the early universe that focus on the dynamical behavior of metal-free gas under different initial and environmental conditions. In particular we investigate the role of turbulence, which is thought to ubiquitously accompany the collapse of high-redshift halos. We distinguish between two main cases: the birth of Population III.1 stars – those which form in the pristine halos unaffected by prior star formation – and the formation of Population III.2 stars – those forming in halos where the gas has an increased ionization fraction. We find that turbulent primordial gas is highly susceptible to fragmentation in both cases, even for turbulence in the subsonic regime, i.e. for rms velocity dispersions as low as 20 % of the sound speed. Fragmentation is more vigorous and more widespread in pristine halos compared to pre-ionized ones. If such levels of turbulent motions were indeed present in star-forming minihalos, Pop III.1 stars would be on average of somewhat lower mass, and form in larger groups, than Pop III.2 stars. We find that fragment masses cover over two orders of magnitude, suggesting that the Population III initial mass function may have been much broader 