Conference "Zeta Functions"June 21 - 25, 2010Moscow, Russia |
Organisers: Michel Balazard (CNRS, Laboratoire Poncelet), Michael Tsfasman (CNRS, Laboratoire Poncelet, Institute for Information Transmission Problems), Alexey Zykin (Laboratoire Poncelet, State University Higher School of Economics)
Thursday 24 June, 15:00 - 16:00
This work is a joint work with Harald Helfgott. Given a subset A of the primes and a positive integer N, we define the relative density delta(N,A) of the set of elements of A less than N as the quotient between the number of elements af A up to N and the number of primes up to N. Ben Green proved that if N is large enough and if the relative density delta(N,A) is large enough (larger than some given function of N converging to zero as N goes to infinity), then there must be a non-trivial three-term arithmetic progression in the set of elements of A less than N. We improve his quantitative result.