2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121133Assuming the Gowers Inverse conjecture and the Möbius conjecture for the finite parameter $s$, Green-Tao verified Dickson's conjecture for lattices which are ranges of linear maps of complexity at most $s$. In this paper, we reformulate Green-Tao's theorem on Dickson's conjecture, and prove that, if $L$ is the range of a linear map of complexity $s$, and $L_1$ is a sublattice of $L$ of finite index, then $L_1$ is the range of a linear map of complexity $s$.Revised on Jan. 5, 2007Number Theory11P32text