33 citations · 41 across the 12 of their papers we have counts for
4 papers · 1 filter
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…
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(…
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…