Rushil Raghavan

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math.NT2026

Improved Bounds for 3-Progressions

Rushil Raghavan

We prove that if $A \subset {1, \dots, N}$ has no nontrivial three-term arithmetic progressions, then $∣ A ∣ \leq exp (- c lo g (N)^{1/6} lo g lo g (N)^{- 1}) N$ for some absolute constant $c>…

math.NT2025

Improved Bounds for the Freiman-Ruzsa Theorem

Rushil Raghavan

Let $A$ be a finite subset of an abelian group $G$ , and suppose that $∣ A + A ∣ \leq K ∣ A ∣$ . We show that for any $ε > 0$ , there exists a constant $C_{ε}$ such that $A$ can be covered by at…