Quadratic forms vs congruences

[Max Alekseyev]

On Thu, Apr 24, 2008 at 2:54 PM, Max Alekseyev <maxale at gmail.com> wrote:

>  >  Has anyone answered this question: what is the latest that sequences of
>  >  this type (quadratic forms and congruences) can disagree?  It seems that
>  >  the answer will depend on the discriminant.
>
>  For the form x^2+n*y^2, exceptional primes are factors of n and
>  Discriminant(f_n(t)) (see Theorem 2.1.1 for details).

btw, even with respect to non-exceptional primes, the statement like
"primes of the form x^2+n*y^2 are those of the form U*k+V" seems to be
possible only if the class number h(-4n) = degree(f_n(t)) does not
exceed 2. For degree(f_n(t)) > 2, there seems to be no direct
relationship between the solveblity of f_n(t) modulo p and the
determinant of f_n(t).
However, I don't have a proof that the case h(-4n)>2 cannot result in
a simple description of the primes represented by x^2+n*y^2.

Regards,
Max