Czechoslovak Mathematical Journal, Vol. 68, No. 1, pp. 169-193, 2018
A higher rank Selberg sieve and applications
Received August 2, 2016. First published December 12, 2017.
Abstract: We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
Keywords: Selberg sieve; bounded gaps; prime $k$-tuples