let $q$ be a non-degenerate indefinite quadratic form over $ \mathbb{r}$ in $n \ge 3$ variables. establishing a longstanding conjecture of oppenheim, margulis proved in 1986 that if $q$ is not a multiple of a rational form, then the set of values $q( \mathbb{z}^n)$ is a dense subset of $ \mathbb{r}$. quantifying this result, eskin, margulis, and mozes proved in 1986 that unless $q$ has signature $(2,1)$ or $(2,2)$, then the number $n(a,b;r)$ of integral vectors $v$ of norm at most $r$ satisfying $q(v) \in (a,b)$ has the asymptotic behavior $n(a,b;r) \sim \lambda(q) \cdot (b-a) r^{n-2}$. now, let $s$ is a finite set of places of $ \mathbb{q}$ containing the archimedean one, and $q=(q_v)_{v \in s}$ is an $s$-tuple of irrational isotropic quadratic forms over the completions $ \mathbb{q}_v$. in this talk i will discuss the question of distribution of values of $q(v)$ as $v$ runes over $s$-balls in $ \mathbb{z}[1/s]$. this talk is based on a joint work with seonhee lim and jiyoung han.