Half-waves and spectral Riesz means on the 3-torus

Elliott Fairchild, Ethan Sussman

For a full rank lattice $\Lambda \subset {\mathbb{R}}^d$ and $\mathbf{A}\in {\mathbb{R}}^d$, consider $N_{d,0;Λ,\mathbf{A}}(Σ) = \# ([Λ+\mathbf{A}] \cap Σ\mathbb{B}^d) = \# \{\mathbf{k}\in Λ…