From the top to the bottom of the main sequence:: A complete mass function of the young open cluster M35

We present very deep and accurate photometry of the open cluster M35. We have observed this association in the Cousins R, I filters, together with the Johnson V filter. We have covered a region of 27.5 x 27.5 square arcmin, equivalent to a fifth of the total area of the cluster. The data range from I-c = 12.5 to 23.5 mag, and the color intervals are 0.4 less than or equal to (V - I)c less than or equal to 3.0, 0.5 less than or equal to (R - I)(c) less than or equal to 2.5. Roughly, these values span from 1.6 M. down to the substellar limit, in the case of cluster members. By using the location of the stars on color-magnitude and color-color diagrams, we have selected candidate members of this cluster. We have merged our sample with previously published data and obtained a color-magnitude diagram for the complete stellar population of the cluster, covering the spectral range early B-mid M. Based on the distribution of field and cluster stars in color-magnitude and color-color diagrams, we estimate that two-thirds of these candidates are likely to be true members of M35. These stars approximately double the number of stars identified as candidate members of this cluster (similar to 2700). We provide the photometry and accurate positions of these stars. The deep photometry has allowed us to study the mass segregation within the cluster, the luminosity function, and mass function. We show that in the magnitude range 13 less than or equal to I-c less than or equal to 22 there is a reduced mass segregation, in opposition to what happens to higher mass stars, where the mass segregation is stronger. The luminosity function behaves essentially as the one characteristic of the Pleiades, presenting a peak at I-c similar to 19 mag (M-I similar to 9). Combining our photometry with previous data corresponding to more massive stars, we find that the mass function increases monotonically, when plotted in a log-log form, until it reaches similar to0.8 M. (alpha = 2.59). It remains shallower for less massive stars (alpha = 0.81 for 0.8-0.2 M.), whereas a decrease is observed for stars close to the substellar regime. These different behaviors suggest that at least three mechanisms play a role in the formation of stellar and substellar objects. The total mass of the cluster is similar to 1600 M. in the area covered by this study.