5 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 no…
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…
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…