Author

Samuel P. Ferguson

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Preprint Oct 2026

Additive energy and Fourier complexity of graphs

We study the additive energy and the Fourier approximation of graph adjacency matrices labeled by a cyclic group. For a graph with $N$ vertices, $s$ edges and adjacency matrix $M$, the additive energy of its directed edge set is at most $\min\{(2s)^3,N^2\operatorname{tr}(M^4)\}$, and equality in the spectral bound hold...

V. Gupta, S. Ferguson, A. Iosevich et al. · 0 citations

Preprint Oct 2026

Fuglede's conjecture holds in $\mathbb{F}_{p}^{d}$ for $p=2,\,d=8$ and $p=11,\,d=3$

Fuglede's conjecture in $\mathbb{F}_p^d$ says that a nonempty set tiles by translation if and only if it is spectral. We prove the conjecture in $\mathbb{F}_2^8$ and $\mathbb{F}_{11}^3$. Over $\mathbb{F}_2$ we show more generally that the Fourier support of a nonconstant indicator of density different from one half con...

S. Ferguson, J. Iosevich · 0 citations