On restriction estimates for discrete quadratic surfaces

Abstract

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.

17 pages. This article is a companion to our previous paper: arXiv:1610.03984, and as such, the methods are similar. So that the articles may be read independently Section 3 of this article is close to Section 6 of arXiv:1610.03984. International Mathematics Research Notices (2018)