Sublattices of finite index

Details Sublattices of finite index Sublattices of finite index

2006-12-15

arxiv.org/abs/math/0612439v4

Mathematics

Number Theory

Revised on Jan. 5, 2007

Scientific paper

Assuming the Gowers Inverse conjecture and the M\"{o}bius 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 $s$.

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