200701Liu Chunlei

#### Prime points in the intersection of two sublattices

Liu Chunlei, Beijing Normal University

Jan 2, 2007, 9:30-11:30pm 中科院数学院大楼509室

Jan 9, 2007, 2:00-4:00pm to be announced

Abstract: A famous and difficult open conjecture of Dickson predicts the

distribution of prime points in a given affine sublattice. Assuming

the Gowers Inverse conjecture and the Mobius conjecture of

finite parameter s, Green-Tao verified Dickson's conjecture for

affine sublattices which are ranges of affine linear maps of

complexity $s$. In this paper, as an application of Green-Tao's

theorem on Dickson's conjecture, we study the distribution of prime

points in affine sublattices of finite index in a given affine

sublattice.