2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/11981Knowledge of the evolution of the low column density end of the Ly alpha forest (12.8 < log N_HI < 16.0 cm^-2) can provide substantial insight for models of structure formation and studies of the evolution of the ionizing background. Here we describe the evolution of the b values and column densities of forest clouds over the redshift range 2 < z < 4. While the distribution function for clouds with column densities N_HI < 3 x 10^14 cm^-2 can be well described by a single invariant power law fit with slope ~-1.5 over this range, at higher column densities a break in this distribution function is seen, with a deficiency of high column density clouds relative to the single power-law fit, and with the break point moving to lower column densities for clouds at lower redshifts. The median and cut-off (minimum) b values are seen to decrease at higher redshifts.6 pages, LaTeX, 4 PostScript figures, uses conf_iap.sty. To appear in the Proceedings of the 13th IAP Colloquium: Structure and Evolution of the IGM from QSO Absorption Line Systems, eds. P. Petitjean and S. CharlotAstrophysicstext