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.