When regarding a ternary quadratic form $Q(x,y,z)$, is a classic question to consider which integers $n$ can be represented by $Q$. It is also classic to wonder how "well distributed" are the lattice points $(x,y,z)\in\mathbb{Z}^3$ that satisfies $Q(x,y,z)=n$ when $n\rightarrow\infty$ along a certain sequence.

When $Q$ is just the modulus square, I have found a lot of literature but I am interested in more general $Q$. On chapter 11 of Topics in Classical Automorphic Forms by Henryk Iwaniec, we find conditions to $n$ so that this condition holds. However, Iwaniec said that the result is due to Duke and that he asked a few less on $n$.

I have tried to read Duke papers:

Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids

And

On ternary quadratic forms,

But I couldn't find the conditions he imposed over $n$ so that we have equidistribution. I am interested in asking the less possible to $n$ and knowing the difference between the hypothesis of Duke and those of Iwaniec.

Thank you to everyone.