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arXiv · 2508.06705

Quadratic forms of signature $(2, 2)$ or $(3, 1)$ I: effective equidistribution in quotients of $\mathrm{SL}_4(\mathbb{R})$

Zuo Lin
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Abstract

We prove an effective equidistribution theorem for orbits of horospherical subgroups of $\mathrm{SO}(2, 2)$ and $\mathrm{SO}(3, 1)$ in quotients of $\mathrm{SL}_4(\mathbb{R})$ with a polynomial error term. In a forthcoming paper, we will use this theorem to prove an effective version of the Oppenheim conjecture for indefinite quadratic forms of signature $(2, 2)$ or $(3, 1)$ with a polynomial error rate.

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Zuo Lin. 2025-08-08. Quadratic forms of signature $(2, 2)$ or $(3, 1)$ I: effective equidistribution in quotients of $\mathrm{SL}_4(\mathbb{R})$. https://arxiv.org/abs/2508.06705

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