On restriction estimates for discrete quadratic surfaces

TL;DR

This paper establishes new truncated restriction estimates for discrete quadratic surfaces defined by indefinite quadratic forms, advancing understanding in harmonic analysis on such algebraic structures.

Contribution

It introduces novel truncated restriction estimates for discrete quadratic surfaces with indefinite quadratic forms, a previously unexplored aspect in harmonic analysis.

Findings

Established truncated restriction estimates for discrete quadratic surfaces

Extended harmonic analysis techniques to indefinite quadratic forms

Provided bounds applicable to integer lattice points on 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.