Alladi Ramakrishnan Hall

Roth's theorem in primes and its generalisation

Gyan Prakash

Harish-Chandra Research Institute

In the last lecture of this lecture series, we shall explain a proof due to Helfgott and Roton of the celebrated result of Ben Green that a dense subset of primes contains infinitely many non-trivial three term arithmetic progression.
We shall show that in fact their arguments leads to a more general result. For an instance, it shows that a dense subset of Chen primes contain infinitely many non-trivial three term arithmetic progression. A prime is said to be Chen prime if p+2 has at-most two prime factors.