Re: Deciphering JSH


Gene Ward Smith wrote:
David C. Ullrich wrote:

It _can't_ mean that. Because there are plenty of people with
PhD's who say the results are wrong (to the extent that they
can figure out what the results _are_, anyway).

To the extent it can be figured out at all, I think you should start
here:

Consider the binary form in x and y (v^3+1)*x^3-3*v*x*y^2+y^3. By
setting x=1, we get an affine version of this, which is a polynomial in
Q(v); that is, a polynomial with coefficients in
an indeterminate v: y^3-3*v*y^2+v^3+1. Now ignore all the useless
bells and whistles introducing m, f, and u. The above polynomial has
discriminant 27*(v^3+1)*(3*v^3-1), and
at v = -1, we can expand the roots in Puiseux series. One of these
expansions will be unramified, involving powers of (v+1), and the other
two are ramified, involving powers of sqrt(v+1). The unramified branch
mutates into the distinguished root on specializing v

Well, duh!

.