Conférence "Zeta Functions"

Improving Roth's theorem in the primes

Anne de Roton (Vancouver)

Jeudi 24 juin, 15:00 - 16:00

Résumé

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.