On the invariant field of binary octavics
The invariant field \(P_ n\) of binary \(n\)-forms over \(\mathbb{C}\) is studied. It is shown that for each even integer \(n\geq 8\) the field \(P_ n\) is generated by \(n-2\) ( = transcendence degree over \(\mathbb{C}\)) rational functions whose denominators are certain powers of some homogeneous invariant polynomial of degree 12. The six generators of the field \(P_ 8\) of binary octavics are also found in detailed form.
scientific article; zbMATH DE number 9218