Diophantine equations in the primes

The affine sieve

(2013) Alireza Salehi Golsefidy et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

Primes in tuples I

(2010) Daniel Goldston et al.   ANNALS OF MATHEMATICS

Linear equations in primes

(2010) Benjamin Green et al.   ANNALS OF MATHEMATICS

A Birch–Goldbach theorem

(2010) J. Brüdern et al.   ARCHIV DER MATHEMATIK

Integral points on quadrics in three variables whose coordinates have few prime factors

(2010) Jianya Liu et al.   ISRAEL JOURNAL OF MATHEMATICS

Integral points on quadrics with prime coordinates

(2010) Jianya Liu   MONATSHEFTE FUR MATHEMATIK

Affine linear sieve, expanders, and sum-product

(2009) Jean Bourgain et al.   INVENTIONES MATHEMATICAE