|Dept.||University of Wisconsin|
Let G = SL(d, R) ⋉ R^d be the affine special linear group of the plane and set Γ = SL(d, Z) ⋉ Z^d.
In this talk, we prove a polynomially effective asymptotic equidistribution result for the orbits of an unstable horospherical unipotent flow on G/Γ.
Strombergsson(2015) settled the case of dimension d=2 by using analytic number theoretic method.
We will use the earlier result of the effective equidistribution on SL(d, R)/SL(d, Z) and an estimate of the oscillatory integral on the fiber to show the general dimension case.