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4 papers
Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond
Boris Alexeev, Kevin Barreto, Yanyang Li +5
A set of integers is primitive if no number in the set divides another. We introduce a new method for bounding Erdős sums of primitive sets, suggested from output of GPT-5.4 Pro, b…
Marton's Conjecture in abelian groups with bounded torsion
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a Freiman--Ruzsa-type theorem with polynomial bounds in arbitrary abelian groups with bounded torsion, thereby proving (in full generality) a conjecture of Marton. Specifi…
On a conjecture of Marton
W. T. Gowers, Ben Green, Freddie Manners +1
We prove a conjecture of K. Marton, widely known as the polynomial Freiman--Ruzsa conjecture, in characteristic . The argument extends to odd characteristic, with details to fol…
The distribution of polynomials over finite fields, with applications to the Gowers norms
Ben Green, Terence Tao
In this paper we investigate the uniform distribution properties of polynomials in many variables and bounded degree over a fixed finite field F of prime order. Our main result is…