On primitive spinor exceptional representations (Q1084128)

In earlier papers a relationship between primitive representations of certain numbers \(c\) by a spinor genus of a ternary quadratic form \(f\) and primitive representations of \(ct^2\), \((t,2D)=1\), by \(f\) was established (\(D\) is the discriminant of \(f\)). This paper gives a generalization of this result to higher dimensional settings, namely to primitive representations of forms by forms, more precisely: a relationship between primitive representations of certain \(n\)-ary quadratic forms \(g\) by a spinor genus of an \((n+2)\)-ary quadratic form \(f\) and primitive representations of some \(n\)-ary subform \(fg'\) of \(g\) by \(f\) itself is established.