collaborators

6 papers

math.NT2026

Lower bounds for some value sets over finite fields: incidence geometry and Bourgain's group expansion theorem

Xiyu Hu

We develop two transition principles for lower-bounding value sets generated by structured sequences over prime fields. A reciprocal-affine family with internal transitions and…

math.NT2026

Improved Weyl bounds on short intervals

Xiyu Hu

For an integer , put . Let be reduced, let , and let be an interval of …

math.CO2026

Lonely Runners over Function Fields: Quantized Phase--Riesz product

Xiyu Hu

Let be the least cardinality of a family of nonzero polynomials over whose associated codimension- partial-circulant kernels cover the full coefficient sp…

math.CA2026

Complexity-sensitive additive energy and off-diagonal Young inequalities on bounded-degree algebraic varieties

Xiyu Hu

We develop additive-energy estimates and weighted Young inequalities for finite sets on bounded-degree real algebraic varieties. For an irreducible -dimensional variety , let…

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 -Hessian Solutions

Xiyu Hu

Let , let be open and convex, and let be a convex viscosity solution of in . We prove that the set on which fails to be…