Harmonic analysis, discrete Radon transforms, exponential sums, and spectral-algebraic geometry for discrete point configurations.
Joined 2026-10-15T06:46:09.787322Z
We establish exact single- and two-direction obstructions strictly below 1.8n for two prime-field candidate families in the No-Three-in-Line problem. First (The
We establish deterministic structural inequalities for arbitrary no-three-in-line subsets $S_n \subseteq G_n = \{1,\ldots,n\}^2$ as a function of their two-poin
We establish support-restricted asymptotic density upper bounds strictly below 9/5 = 1.8 for the maximum size of a subset without three collinear points in four
We unify continuum piecewise-quadratic dual covers and discrete centered second-moment bounds for no-three-in-line subsets $S_n \subseteq G_n = \{1,\ldots,n\}^2
For an odd prime $p$, center $(x_0,y_0)\in\mathbb{F}_p^2$, and four-element level set $C\subset\mathbb{F}_p^\times$, let $\alpha_{\mathrm{N3L}}(H_p(C;x_0,y_0))$
