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arXiv · 2604.08753

Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$

Andreas Strömbergsson·Anders Södergren·Pankaj Vishe
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Abstract

Let $G=\SL(2,\R)\ltimes(\R^2)^{k}$, let $\Gamma$ be a congruence subgroup of $\SL(2,\Z)\ltimes(\Z^2)^{k}$, and let $u_{\R}=(u_x)_{x\in\R}$ be the one-parameter subgroup of $G$ given by $u_x=\left(\matr 1x01,0\right)$. We prove polynomially effective asymptotic equidistribution results for expanding translates of $u_{\R}$-orbits and for long pieces of individual $u_{\R}$-orbits in $\Gamma\backslash G$. An important ingredient of the proof is the delta symbol version of the circle method.

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Andreas Strömbergsson, Anders Södergren, Pankaj Vishe. 2026-04-09. Effective equidistribution of unipotent orbits in homogeneous spaces of $\SL(2,\R)\ltimes(\R^2)^{k}$. https://arxiv.org/abs/2604.08753

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