Number Theory Seminar

Tuesday 23 November 2004

Ben Green (Cambridge)
Quadratic fourier analysis and the primes

I would like to outline a program of research that I am currently undertaking with Terry Tao. One aim of this is to establish an asymptotic for the number of k-tuples of primes p_1 < p_2 < ... < p_k < N in arithmetic progression, or more generally for the number of solutions to k-2 simultaneous linear equations in k prime unknowns. This would be an extension of the "Hardy-Littlewood method" to problems far beyond the reach of the method in its classical form. The program has been successful in the case k = 4, and we shall outline some of that theory.