Hello,
this problem is still unsolved.
If you have any hints or ideas, it would be great if you would answer.
Bye,
Alexander
Hi,
for which primes are the quadratic forms
and
isotropic over the field over -adic numbers ?
A abbreviated form for the two quadratic forms above is and .
Define .
I can use the fact that a regular quadratic form over a field is isotropic if and
.
[ denotes the Hilbert symbol and the discriminant of .]
Moreover, a regular quadratic form over a field is isotropic if and
or { and }.
means actually that the residue classes of and are not equal modulo .
Let's come to the first form:
, therefore .
Now I have to check for which primes
in .
But I don't know how to solve it.
Please can you help me?
Thanks!
Regards
Alexander