Im trying to show that the binary form $x^{n−1}+x^{n−2}yα+x^{n−3}y^2α^2+...+y^{n−1}α^{n−1}$ is bounded below by $ c*y^{n−1}$ where c is some explicit constant.
For the case n=3 this is fairly easy, using the discrimiant of the binary quadratic form, $c=3/4\alpha^2 $
Yes this equation is from the factorization of $x^n-(\alpha y)^n$ and it is of degree n-1