The discrete restriction conjecture for lattice points on spheres

Let $n \geq 3$, let $\lambda \geq 1$, and let $S^{n-1}$ denote the unit sphere in $\mathbb{R}^n$. For a function $f$ on $\mathbb{T}^n$, write $\widehat f(k)$ for its Fourier coefficient at $k \in \mathbb{Z}^n$. Discrete restriction conjecture. For every $\varepsilon > 0$,

\Big\\| \sum_{k \in \mathbb{Z}^n \cap \lambda S^{n-1}} \widehat{f}(k)e^{2\pi i x \cdot k} \Big\\|_{L^{\frac{2n}{n-2}}(\mathbb{T}^n)} \lesssim_{\varepsilon} \lambda^{\varepsilon} \\|f\\|_{L^2(\mathbb{T}^n)}.

This is a discrete Fourier restriction estimate for lattice points on spheres and is presented as related to the spectral projection and resolvent estimates discussed in the paper. Its status is not resolved in the supplied text.