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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.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…