Lower Bounds on Binary Forms of degree m

The following paper http://www.math.leidenuniv.nl/~evertse/05-discres.pdf looks at the binary form $\sum \alpha_ix^iy^{m-i} where i ranges from 0 to m. It then defines the discriminant.

It's well known that for binary quadratic forms how to find a lower bound using the discriminant. I was wondering if analogous theorems hold for a form of arbitrary degree.

Ultimately I would like to find a lower bound in terms of the variable y for this binary form I'm working on.

A little more details:

I'm trying to show that the binary form $x^{n-1}+x^{n-2}y\alpha^2+x^{n-3}y^2\alpha^3+...+y^{n-1}\alpha^{n-1}$ is bounded below by $c*y^{n-1}$ or something similar where c is some explicit constant.

edited Apr 30 2012 at 21:08

asked Apr 30 2012 at 20:43

Kale
99●2

Something odd about the alphas in the last formula. Are those supposed to be exponents on the alphas, or subscripts (as in the first sentence of the question)? And are they supposed to match the exponents on $y$ (as in the first and last terms), or keep 1 ahead (as in the second and third terms)? Please edit the question. – Gerry Myerson Apr 30 2012 at 23:43

Also posted to m.se, math.stackexchange.com/questions/139119/…, without reference to the post here. That's very rude. – Gerry Myerson May 1 2012 at 0:08