17 citations · 81 across the 12 of their papers we have counts for
12 papers
Second moment of the light-cone Siegel transform and applications
Dubi Kelmer, Shucheng Yu
We study the light-cone Siegel transform, transforming functions on the light cone of a rational indefinite quadratic form to a function on the homogenous space $\text{SO}^+_Q(…
Fourier expansion of light-cone Eisenstein series
Dubi Kelmer, Shucheng Yu
In this work we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n+1-space. As a consequ…
A measure estimate in geometry of numbers and improvements to Dirichlet's theorem
Dmitry Kleinbock, Andreas Strömbergsson, Shucheng Yu
Let be a continuous decreasing function defined on all large positive real numbers. We say that a real matrix is -Dirichlet if for every sufficiently large r…
Quantitative Diophantine approximation with congruence conditions
Mahbub Alam, Anish Ghosh, Shucheng Yu
In this short paper we prove a quantitative version of the Khintchine-Groshev Theorem with congruence conditions. Our argument relies on a classical argument of Schmidt on counting…
Translates of rational points along expanding closed horocycles on the modular surface
Claire Burrin, Uri Shapira, Shucheng Yu
We study the limiting distribution of the rational points under a horizontal translation along a sequence of expanding closed horocycles on the modular surface. Using spectral meth…
Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts
Anish Ghosh, Dubi Kelmer, Shucheng Yu
We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed quadratic forms and generic shifts. Our results…
Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts
Anish Ghosh, Dubi Kelmer, Shucheng Yu
We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When…
A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem
Dmitry Kleinbock, Shucheng Yu
Let be the space of unimodular lattices in , and for any denote by the s…
Values of random polynomials in shrinking targets
Dubi Kelmer, Shucheng Yu
Relying on the classical second moment formula of Rogers we give an effective asymptotic formula for the number of integer vectors in a ball of radius , with value in…
The second moment of the Siegel transform in the space of symplectic lattices
Dubi Kelmer, Shucheng Yu
Using results from spectral theory of Eisenstein series, we prove a formula for the second moment of the Siegel transform when averaged over the subspace of symplectic lattices. Th…
Shrinking targets problems for flows on homogeneous spaces
Dubi Kelmer, Shucheng Yu
We study shrinking targets problems for discrete time flows on a homogenous space with a semisimple group and an irreducible lattice. Our results apply to b…
Logarithm laws for unipotent flows on hyperbolic manifolds
Shucheng Yu
We prove logarithm laws for unipotent flows on non-compact finite-volume hyperbolic manifolds. Our method depends on the estimate of norms of certain incomplete Eisenstein series.