A uniform Linnik basic lemma and entropy bounds
Number Theory
2025-08-05 v2 Dynamical Systems
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.
Cite
@article{arxiv.2201.05380,
title = {A uniform Linnik basic lemma and entropy bounds},
author = {Andreas Wieser and Pengyu Yang},
journal= {arXiv preprint arXiv:2201.05380},
year = {2025}
}
Comments
Final version. To appear in Commentarii Math. Helv