A consequence of the factorisation theorem for polynomial orbits on nilmanifolds
arXiv:1509.06030
Abstract
We discuss a consequence of Green and Tao's factorisation theorem for polynomial orbits on nilmanifolds, adjusted to the requirements of certain arithmetic applications. More precisely, we prove a generalisation of Theorem 16.4, Acta Arith. 154 (2012), 235-306, by slightly rearranging its proof. The thus achieved strengthening of the result removes an oversight in the above-cited paper which resulted from the previously too weak conclusion. Since this type of result proved essential for further applications, we take the opportunity to discuss it in more detail.
Corrigendum to Acta Arith. 154 (2012), 235-306 (arXiv:1106.4690)