A uniform Linnik basic lemma and entropy bounds
arXiv:2201.05380
Abstract
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(12), 2019). As an application, we establish entropy bounds for limits of invariant measures on homogeneous toral sets in GL(4) of biquadratic, cyclic, or dihedral type.
Final version. To appear in Commentarii Math. Helv