CNRS Poncelet

Конференция "Дзета функции"

21 - 25 июня, 2010

Москва, Россия

RAS Poncelet

Организаторы: Michel Balazard (CNRS, Лаборатория Понселе), Михаил Цфасман (CNRS, Лаборатория Понселе, ИППИ РАН), Алексей Зыкин (Лаборатория Понселе, ГУ ВШЭ)

English French

Improving Roth's theorem in the primes

Anne de Roton (Ванкувер)

Четверг 24 июня, 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.

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