Effective equidistribution for some one parameter unipotent flows
Abstract
We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2 (\mathbb{R})$ in arithmetic quotients of $\mathrm{SL}_2 (\mathbb{C})$ and $\mathrm{SL}_2 (\mathbb{R}) \times \rm{SL}_2(\mathbb{R})$. The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Algebraic Geometry and Number Theory
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Annals of Mathematics
- Publisher
- Annals of Mathematics
- Volume
- 204
- Issue
- 2
- Pages
- 603–740
- Publication date
- 1 September 2026
- Language
- EN