Pointwise convergence in nilmanifolds along smooth functions of polynomial growth
Pointwise convergence in nilmanifolds along smooth functions of polynomial growth
Abstract We study the equidistribution of orbits of the form $b_1^{a_1(n)}\cdots b_k^{a_k(n)}\Gamma $ in a nilmanifold X , where the sequences $a_i(n)$ arise from smooth functions of polynomial growth belonging to a Hardy field. We show that under certain assumptions on the growth rates of the functions $a_1,\ldots ,a_k$ , …