arXiv subjects

Shucheng Yu

Publications and source records attributed to Shucheng Yu.

21 records · Page 2Linked to original sources

arXiv2018

The second moment of the Siegel transform in the space of symplectic lattices

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. This generalizes the classical formula of Rogers for the second moment in the full space of unimodular lattices. Using this new formula we give very strong bounds for the discrepancy of the number of lattice points in an Borel set, which hold for generic symplectic lattices.

math.NT↗

arXiv2017

Shrinking targets problems for flows on homogeneous spaces

We study shrinking targets problems for discrete time flows on a homogenous space $Γ\backslash G$ with $G$ a semisimple group and $Γ$ an irreducible lattice. Our results apply to both diagonalizable and unipotent flows, and apply to very general families of shrinking targets. As a special case, we establish logarithm laws for cusp excursions of unipotent flows answering a question of Athreya and Margulis.

math.DS↗

arXiv2017

Logarithm laws for unipotent flows on hyperbolic manifolds

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.

math.DS↗