The generating series of the Bass numbers $\mu^i_R=\mathrm{ rank}_k \mathrm{ Ext}^i_R(k,R)$ of local rings $R$ with residue field $k$ are computed in closed rational form, in case the embedding dimension $e$ of $R$ and its depth $d$ satisfy $e-d\le 3$. For each such $R$ it is proved that there is a real number $\gamma>1$, such that $\mu^{ d+i}_R\ge\gamma\mu^{ d+i-1}_R$ holds for all $i\ge 0$, except for $i=2$ in two explicitly described cases, where $\mu^{ d+2}_R=\mu^{ d+1}_R=2$. New restrictions are obtained on the multiplicative structures of minimal free resolutions of length 3 over regular local rings.
Categories: math.AC math.KT math.RA