4 citations · 10 across the 10 of their papers we have counts for
10 papers
Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields
Jiyoung Han, Noy Soffer Aranov
We prove a quantitative version of Oppenheim's conjecture in the function field setting. In order to do so, we compute the higher moments of the Siegel transform. In particular, we…
A quantitative Khintchine-Groshev theorem for S-arithmetic Diophantine approximation
Jiyoung Han
In his 1960 paper, Schmidt studied a quantitative type of Khintchine-Groshev theorem for general (higher) dimensions. Recently, a new proof of the theorem was found, which made it…
Asymptotic distribution for pairs of linear and quadratic forms at integral vectors
Jiyoung Han, Seonhee Lim, Keivan Mallahi-Karai
We study the joint distribution of values of a pair consisting of a quadratic form and a linear form over the set of integral vectors, a problem initiated by Dani-M…
Higher moment formulae and limiting distributions of lattice points
Mahbub Alam, Anish Ghosh, Jiyoung Han
We prove functional limit theorems for lattice point counting for affine and congruence lattices using the method of moments. Our main tools are higher moment formulae for Siegel t…
Values of Inhomogeneous Forms at S-integral points
Anish Ghosh, Jiyoung Han
We prove effective versions of Oppenheim's conjecture for generic inhomogeneous forms in the S-arithmetic setting. We prove an effective result for fixed rational shifts and generi…
A generic effective Oppenheim theorem for systems of forms
Prasuna Bandi, Anish Ghosh, Jiyoung Han
We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several line…
Rogers' mean value theorem for -arithmetic Siegel transform and applications to the geometry of numbers
Jiyoung Han
We prove higher moment formulas for Siegel transforms defined over the space of unimodular -lattices in , , where in the real case, the formulas are intro…
Quantitative Oppenheim conjecture for -arithmetic quadratic forms of rank and
Jiyoung Han
The celebrated result of Eskin, Margulis and Mozes (1998) and Dani and Margulis (1993) on quantitative Oppenheim conjecture says that for irrational quadratic forms of rank at…
Asymptotic distribution of values of isotropic quadratic forms at -integral points
Jiyoung Han, Seonhee Lim, Keivan Mallahi-Karai
We prove an analogue of a theorem of Eskin-Margulis-Mozes: suppose we are given a finite set of places over containing the archimedean place and excluding the prim…
Distribution of integral lattice points in an ellipsoid with a diophantine center
Jiyoung Han, Hyunsuk Kang, Yong-Cheol Kim +1
We evaluate the mean square limit of exponential sums related with a rational ellipsoid, extending a work of Marklof. Moreover, as a result of it, we study the asymptotic values of…