## Number Theory Seminar

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Tuesday 23 November 2004

Ben Green (Cambridge)

Quadratic fourier analysis and the primes

Abstract:

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.