  The Herschel Gould Belt survey mapped the nearby (d < 500 pc) star-forming
regions to understand better how the prestellar phase influences the star
formation process. Here we report a complete census of dense cores in a 15 deg2
area of the Serpens star-forming region located between d=420 pc and 484 pc.
The PACS and SPIRE cameras imaged this cloud from 70micron to 500micron. With
the multi-wavelength source extraction algorithm getsources, we extract 833
sources, of which 709 are starless cores and 124 are candidate proto-stellar
cores. We obtain temperatures and masses for all the sample, classifying the
starless cores in 604 prestellar cores and 105 unbound cores. Our census of
sources is 80% complete for masses larger than 0.8 Msun overall. We produce the
core mass function (CMF) and compare it with the initial mass function (IMF).
The prestellar CMF is consistent with log-normal trend up to 2 Msun, after
which it follows a power-law with slope of -2.05+/-0.34. The tail of its CMF is
steeper but still compatible with the IMF for the region we studied in this
work. We also extract the filaments network of the Serpens region, finding that
81% of prestellar cores lie on filamentary structures. The spatial association
between cores and filamentary structure supports the paradigm, suggested by
otherHerschelobservations, that prestellar cores mostly form on filaments.
Serpens is confirmed to be a young, low-mass and active star-forming region.
