A Turn-over in the Galaxy Luminosity Function of the Coma Cluster Core?

8 pages, 6 postscript figures, accepted in A&A, new table 1, updated figuresOur previous study of the faint end (R$\\leq$21.5) of the galaxy luminosity function (GLF) was based on spectroscopic data in a small region near the Coma cluster center. In this previous study Adami et al. (1998) suggested, with moderate statistical significance, that the number of galaxies actually belonging to the cluster was much smaller than expected. This led us to increase our spectroscopic sample. Here, we have improved the statistical significance of the results of the Coma GLF faint end study (R$\\leq$22.5) by using a sample of 85 redshifts. This includes both new spectroscopic data and a literature compilation. The relatively small number of faint galaxies belonging to Coma that was suggested by Adami et al. (1998) and Secker et al. (1998) has been confirmed with these new observations. We also confirm that the color-magnitude relation is not well suited for finding the galaxies inside the Coma cluster core, close to the center at magnitudes fainter than R$\\sim$19. We show that there is an enhancement in the Coma line of sight of field galaxies compared to classical field counts. This can be explained by the contribution of groups and of a distant $z\\sim 0.5$ cluster along the line of sight. The result is that the Coma GLF appears to turn-over or at least to become flat for the faint galaxies. We suggest that this is due to environmental effects