Jiyoung Han

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math.NT2025

Moment formulas of Siegel transforms with congruence conditions in dimension 2

Jiyoung Han, Seul Bee Lee

We compute the first and second moment formulas for Siegel transforms related to problems counting primitive lattice points in the real plane with congruence conditions. As applica…

math.NT2025

Mean value theorems for the S-arithmetic primitive Siegel transforms

Samantha Fairchild, Jiyoung Han

We develop the theory and properties of primitive unimodular $S$ -arithmetic lattices in $Q_{S}^{d}$ by giving integral formulas in the spirit of Siegel's primitive mean value…

math.NT2024

Distribution of Primitive Lattice Points in Large Dimensions

Jiyoung Han

We investigate the asymptotic behavior of the distribution of primitive lattice points in a symmetric Borel set $S_{d} \subset R^{d}$ as $d$ goes to infinity, under certain volum…