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The origin of the stellar initial mass function (IMF) is one of the mostdebated issues in astrophysics.  Here, we explore the possible link between the quasi-universal filamentarystructure of star-forming molecular clouds and the origin of the IMF.  Based on our recent comprehensive study of filament properties from HerschelGould Belt survey observations (Arzoumanian et al.), we derive, for the firsttime, a good estimate of the filament mass function (FMF) and filament linemass function (FLMF) in nearby molecular clouds. We use the observed FLMF topropose a simple toy model for the origin of the prestellar core mass function(CMF), relying on gravitational fragmentation of thermally supercritical butvirialized filaments.  We find that the FMF and the FLMF have very similar shapes and are bothconsistent with a Salpeter-like power-law function (d$N$/dlog$M_{\rm line}\propto M_{\rm line}^{-1.5\pm0.1}$) in the regime of thermally supercriticalfilaments ($M_{\rm line} > 16\, M_\odot$/pc). This is a remarkable resultsince, in contrast, the mass distribution of molecular clouds and clumps isknown to be significantly shallower than the Salpeter power-law IMF, withd$N$/dlog$M_{\rm cl} \propto M_{\rm cl}^{-0.7}$.  Since the vast majority of prestellar cores appear to form in thermallytranscritical or supercritical filaments, we suggest that the prestellar CMFand by extension the stellar IMF are at least partly inherited from the FLMFthrough gravitational fragmentation of individual filaments.

The role of molecular filaments in the origin of the prestellar core mass function and stellar initial mass function