33 citations · 41 across the 12 of their papers we have counts for
12 papers
Hausdorff dimension of non-uniquely ergodic directions in eigenform loci
Yuming Wei, Pengyu Yang
We consider the eigenform locus in where is not a square. We prove that for any translation surface , the set of non…
Birkhoff genericity on affine subspaces in horospheres
Nimish A. Shah, Pengyu Yang
We study Birkhoff genericity for a simple uniformly expanding diagonal flow on , with initial points restricted to affine…
Representations of binary quadratic forms by quaternary quadratic forms
Wooyeon Kim, Andreas Wieser, Pengyu Yang
We prove a local-global principle for primitive representations of binary quadratic forms by quaternary quadratic forms. Our method is a variant of Linnik's ergodic method showing…
An upper bound of the Hausdorff dimension of singular vectors on affine subspaces
Nimish A. Shah, Pengyu Yang
In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of $\mathbb{R}^n…
Equidistribution of non-uniformly stretching translates of shrinking smooth curves and weighted Dirichlet approximation
Nimish A. Shah, Pengyu Yang
We show that under the action of , where , on the space of unimodular lattices…
A uniform Linnik basic lemma and entropy bounds
Andreas Wieser, Pengyu Yang
We prove a version of Linnik's basic lemma uniformly over the base field using theta-series and geometric invariant theory in the spirit of Khayutin's approach (Duke Math. J., 168(…
Equidistribution of expanding degenerate manifolds in the space of lattices
Nimish A. Shah, Pengyu Yang
For the space of unimodular lattices in a Euclidean space, we give necessary and sufficient conditions for equidistribution of expanding translates of any real-analytic submanifold…
Equidistribution in the space of 3-lattices and Dirichlet-improvable vectors on planar lines
Dmitry Kleinbock, Nicolas de Saxcé, Nimish A. Shah +1
Let , and . Let denote the push-forward of the normalized Lebesgue measure on a segm…
Equidistribution of expanding translates of curves and Diophantine approximation on matrices
Pengyu Yang
We study the general problem of equidistribution of expanding translates of an analytic curve by an algebraic diagonal flow on the homogeneous space of a semisimple algebraic…
Rational points on certain homogeneous varieties
Pengyu Yang
Let be a simply-connected simple connected algebraic group over a number field , and be a semisimple absolutely maximal connected -subgroup of . Under a cohomologi…
Limit distributions of expanding translates of shrinking submanifolds and non-improvability of Dirichlet's approximation theorem
Nimish A. Shah, Pengyu Yang
On the space of unimodular lattices in , we consider the standard action of $a(t)=\mathrm{diag}(t^n,t^{-1},\ldots,t^{-1})\in \mathrm{SL}(n+1,\…
Fundamental Limits of Coded Linear Transform
Sinong Wang, Jiashang Liu, Ness Shroff +1
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed…