276 citations · 4.5k across the 293 of their papers we have counts for
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New bounds for Szemeredi's theorem, II: A new bound for
Ben Green, Terence Tao
Define to be the largest cardinality of a set in which does not contain four elements in arithmetic progression. In 1998 Gowers proved that $r_4(N) \ll…
The primes contain arbitrarily long polynomial progressions
Terence Tao, Tamar Ziegler
We establish the existence of infinitely many \emph{polynomial} progressions in the primes; more precisely, given any integer-valued polynomials $P_1, >..., P_k \in \Z[\m]$ in one…
Linear Equations in Primes
Ben Green, Terence Tao
Consider a system Ψof non-constant affine-linear forms ψ_1,...,ψ_t: Z^d -> Z, no two of which are linearly dependent. Let N be a large integer, and let K be a convex subset of [-N,…
Quadratic Uniformity of the Mobius Function
Ben Green, Terence Tao
This paper is a part of our programme to generalise the Hardy-Littlewood method to handle systems of linear questions in primes. This programme is laid out in our paper Linear Equa…