Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation .
If turbulence driven fragmentation is the mechanism responsible for their formation , we expect their stellar mass function to follow a power-law of slope close to -2 .
We test this hypothesis performing the first analysis of the stellar mass function of clumps hosted in galaxies at z \sim 1 - 3.5 .
The clump sample is gathered from the literature with similar detection thresholds and stellar masses determined in a homogeneous way .
To overcome the small number statistics per galaxy ( each galaxy hosts up to a few tens of clumps only ) , we combine all high-redshift clumps .
The resulting clump mass function follows a power-law of slope \sim - 1.7 and flattens at masses below 2 \times 10 ^ { 7 } M _ { \sun } .
By means of randomly sampled clump populations , drawn out of a power-law mass function of slope -2 , we test the effect of combining small clump populations , detection limits of the surveys , and blending on the mass function .
Our numerical exercise reproduces all the features observed in the real clump mass function confirming that it is consistent with a power-law of slope \simeq - 2 .
This result supports the high-redshift clump formation through fragmentation in a similar fashion as in local galaxies , but under different gas conditions .