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

Andreas Strömbergsson, Anders Södergren, Pankaj Vishe

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 $u_{\mathbb{R}}=(u_x{)}_{x\in \mathbb{R}}$ be the one-parameter subgroup of $G$ given by…