In Proposition 3.3 of the paper: A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan Graphs, Combinatorica 8(1988), the authors use a result obtained by Malisev :
"Let $f(x_1,\ldots,x_n)$ be a quadratic form in $n\geq4$ variables with integer coefficients and discriminant $d$. Let $g$ be an integer prime to $2d$ then if $m$ is sufficiently large with $(g,2md) = 1$, $m$ generic for $f$, and if $(b_1,\ldots,b_n,g)=1, f(b_1,\ldots,b_n)\equiv m(\text{mod } g)$ then there are integers $(a_1,\ldots,a_n)\equiv(b_1,\ldots,b_n) (\text{mod } g)$ with $f(a_1,\ldots,a_n)=m.$"
What does '$m$ generic for $f$' mean? I tried searching for the paper by Malisev or Malyshev, On the representation of integers by positive definite forms, Mat. Steklov (1962) but I can't get hold of it. Please help.
I realize this response is quite late, but just in case anyone else stumbles upon this question: In the book Some applications of modular forms (1990), where the same material is presented in chapter 3, P. Sarnak explains the terminology:
"Let $(g,2d) = 1$ be such that for $m$ sufficiently large with $(g, 2md) = 1$ and $m$ generic for $f$ (i.e., $f = m$ may be solved $\mod \ell$ for every $\ell$) [...]"
Unfortunately, I can't find Malyzev's article anywhere either.