On restriction estimates for discrete quadratic surfaces

We obtain truncated restriction estimates of an unexpected form for discrete surfaces \begin{align} S = {, ( n_1 , \dots , n_d , R( n_1 , \dots, n_d ) ) ,,, n_i \in [-N,N] \cap $\mathbb{Z}$ ,}, \end{align} where $R$ is an indefinite quadratic form with integer matrix.