3 papers
math.DS2026
On Alweiss's example for multiple recurrence
Ben Green
In this expository note we discuss the example of R.~Alweiss giving a construction of a set which intersects every nil-Bohr set, but which is not a set of $2…
math.NT2026
Sumsets and entropy revisited
Ben Green, Freddie Manners, Terence Tao
The entropic doubling of a random variable taking values in an abelian group is a variant of the notion of the doubling constant of a f…
math.CO2026
An inverse theorem for the Gowers U^{s+1}[N]-norm
Ben Green, Terence Tao, Tamar Ziegler
We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we es…