Connections between reduced Bass numbers and Auslanderʹs δ-invariant

We introduce reduced Bass numbers and show that, in the Gorenstein case, the top one coincides with one of the invariants which Auslander and Buchweitz attached to finitely generated modules over such a ring. The other one is Auslanderʹs δ-invariant; we connect the two and treat them in parallel. Finally we demonstrate their relevance to Hochsterʹs Canonical Element Conjecture.