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arXiv · 2506.06948

Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications

Pratyush Sarkar
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Abstract

Let $\Gamma < G$ be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such $G$ of rank at most $2$, in particular $G = \operatorname{SL}_3(\mathbb R)$, we prove effective equidistribution of large translates of tori in $G/\Gamma$. As an application, we obtain an asymptotic counting formula with a power saving error term for integral $3 \times 3$ matrices with a specified characteristic polynomial. These effectivize celebrated theorems of Eskin-Mozes-Shah.

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Pratyush Sarkar. 2025-06-07. Effective equidistribution of translates of tori in arithmetic homogeneous spaces and applications. https://arxiv.org/abs/2506.06948

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