16:30
Linear equations in primes
Abstract
I shall report on a programme of research which is joint with Terence Tao. Our
goal is to count the number of solutions to a system of linear equations, in
which all variables are prime, in as much generality as possible. One success of
the programme so far has been an asymptotic for the number of four-term
arithmetic progressions p_1 < p_2 < p_3 < p_4 <= N of primes, defined by the
pair of linear equations p_1 + p_3 = 2p_2, p_2 + p_4 = 2p_3. The talk will be
accessible to a general audience.