Author

Xin-Hang Ji

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Preprint Sep 2026

A Central Limit Theorem for Coprime Pair Counts in Randomly Translated Disks

We study the distribution of the number of coprime lattice points in randomly translated disks. We prove that its spatial variance is asymptotic to $\sigma^2r\log r$ and establish a central limit theorem under the corresponding normalization, where $\sigma^2$ is an explicit positive constant. By truncating the numerato...

Xin-Hang Ji · 0 citations

Preprint Aug 2026

Shifted second moment of Gaussian Hecke $L$-functions $L(s,\lambda^k)$

We establish a uniform asymptotic formula for the smoothly weighted shifted second moment of the Gaussian angular Hecke $L$-functions $L(s,\lambda^k)$. The completed moment is expressed as the sum of four explicit main terms, corresponding to the four functional-equation swaps, with an error of size $O_{\Phi,\epsilon}(...

Xin-Hang Ji · 0 citations

Preprint Aug 2026

Normal and Lognormal Asymptotics for Lattice-Point Counts in Random Translates of High-Dimensional Balls

Let the center of a $d$-dimensional Euclidean ball be uniformly distributed modulo $\mathbb Z^d$. We study the resulting number of integer lattice points as the dimension and radius tend to infinity. The critical scale is $4\pi^2R_d^2/(d+2)=\log d$. In a logarithmic window around this scale, the logarithm of the lattic...

Xin-Hang Ji · 2 citations