Annals of Mathematics· 2026Q1
Effective equidistribution for some one parameter unipotent flows
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- Q1SCImago
- 2026year
Short summary
New effective equidistribution theorems with polynomial error rates are proven for unipotent flows in specific arithmetic quotients, using Margulis functions and spectral gap tools.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proves effective equidistribution theorems for unipotent flows.
- Achieves polynomial error rates in the equidistribution.
- Applies to orbits in arithmetic quotients of SL2(C) and SL2(R) x SL2(R).
- Utilizes Margulis functions, incidence geometry, and spectral gap.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Annals of Mathematics, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics