Shucheng Yu

collaborators

4 papers

math.NT2019

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…

math.DS2019

A dynamical Borel-Cantelli lemma via improvements to Dirichlet's theorem

Dmitry Kleinbock, Shucheng Yu

Let $X ≅ SL_{2} (R) / SL_{2} (Z)$ be the space of unimodular lattices in $R^{2}$ , and for any $r \geq 0$ denote by $K_{r} \subset X$ the s…

math.NT2018

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 $v$ in a ball of radius $t$ , with value $Q (v)$ in…

math.NT2018

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…