Xiyu Hu

collaborators

2 papers

math.NT2026

Factorial residues modulo a prime: beyond the square-root bound

Xiyu Hu

For a prime $p$, let $A_p=\{k!\pmod p:1\leq k<p\}$. We prove $|A_p|\gg p^{8/15}$, improving the general lower bound $(\sqrt{2}-o(1))p^{1/2}$. The proof begins with the iden…

math.AP2026

Sharp Hausdorff Bounds for the Interior Singular Set of Convex $k$ -Hessian Solutions

Xiyu Hu

Let $2 \leq k \leq n$ , let $I^c ◯ \subset R^{n}$ be open and convex, and let $u$ be a convex viscosity solution of $I ¨ _{k} (D^{2} u) = 1$ in $I^c ◯$ . We prove that the set on which $u$ fails to…

Factorial residues modulo a prime: beyond the square-root bound

Sharp Hausdorff Bounds for the Interior Singular Set of Convex k-Hessian Solutions

Sharp Hausdorff Bounds for the Interior Singular Set of Convex $k$ -Hessian Solutions