On forms in prime variables

Diophantine equations in primes: Density of prime points on affine hypersurfaces

(2022) Shuntaro Yamagishi   DUKE MATHEMATICAL JOURNAL

Quadratic forms and systems of forms in many variables

(2018) Simon L. Rydin Myerson   INVENTIONES MATHEMATICAE

Nested efficient congruencing and relatives of Vinogradov's mean value theorem

(2018) Trevor D. Wooley   PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

Improvements in Birch’s theorem on forms in many variables

(2017) T. D. Browning et al.   JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK

Forms in many variables and differing degrees

(2017) Tim Browning et al.   JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY

Proof of the main conjecture in Vinogradov's Mean Value Theorem \break for degrees higher than three

(2016) Jean Bourgain et al.   ANNALS OF MATHEMATICS

Small gaps between primes

(2015) James Maynard   ANNALS OF MATHEMATICS

Bounded gaps between primes

(2014) Yitang Zhang   ANNALS OF MATHEMATICS

Cubic hypersurfaces and a version of the circle method for number fields

(2014) T. D. Browning et al.   DUKE MATHEMATICAL JOURNAL

Diophantine equations in the primes

(2014) Brian Cook et al.   INVENTIONES MATHEMATICAE

On the Waring-Goldbach problem for fourth and sixth powers

(2014) Lilu Zhao   PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

Vinogradov's mean value theorem via efficient congruencing

(2012) Trevor Wooley   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

The primes contain arbitrarily long arithmetic progressions

(2009) Benjamin Green et al.   ANNALS OF MATHEMATICS

Affine linear sieve, expanders, and sum-product

(2009) Jean Bourgain et al.   INVENTIONES MATHEMATICAE