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We present the galaxy rest-frame near-IR Luminosity Function (LF) and itscosmic evolution to z=1.5 based on a spectroscopic survey of a magnitudelimited sample of galaxies with Ks<20 (the K20 survey, Cimatti et al. 2002b).The LFs have been derived in the rest-frame J and Ks bands using 3 z bins(z_mean= 0.5, 1, 1.5) and compared to the local near-IR LF. The faint-end ofthe LFs is consistent with the local estimates, with no evidence for a changeeither in the slope or normalization up to z<1.3. Viceversa, the density ofluminous galaxies (M_Ks-5logh_70<-25.5) is higher than locally at all z andrelatively constant or mildly increasing with z within our sample. The data areconsistent with a mild luminosity evolution both in the J and Ks-band up toz=1.5 (DeltaM_J=-0.69+-0.12 and DeltaM_K=-0.54+-0.12 at z=1). Moreover, we findthat red and early-type galaxies dominate the bright-end of the LF, and thattheir number density shows at most a small decrease (<30%) up to z=1, thussuggesting that massive elliptical galaxies were already in place at z=1 andthey should have formed their stars and assembled their mass at higher z. Thereappears to be a correlation of the optical/near-IR colors with near-IRluminosities, the most luminous/massive galaxies being red/old. We find a slowevolution with z of the near-IR comoving luminosity density to z=1.5. Finally,we show that hierarchical models overpredict significantly the density of lowluminosity galaxies at z<=1 and underpredict the density of luminous galaxiesat z>=1, whereas PLE models are more consistent with the data up to z=1.5. TheGIF model (Kaufmann et al. 1999) shows a clear deficiency of red luminousgalaxies at z=1 compared to our observations and predicts a decrease ofluminous galaxies with z not observed in our sample.Comment: 13 pages, 13 figures. To appear in Astronomy & Astrophysics. Replaced  by the printed versio

The K20 survey. V. The evolution of the near-IR Luminosity Function