Thomas F. Bloom

most citedAn improvement to the Kelley-Meka bounds on three-term arithmetic progressions

4 citations · 4 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2025

Integers with small digits in multiple bases

Thomas F. Bloom, Ernie Croot

We show that, for any $r \geq 1$ , if $g_{1}, \dots, g_{r}$ are distinct coprime integers, sufficiently large depending only on $r$ , then for any $ε > 0$ there are infinitely many integers…

math.CO2025

Additive structure in convex sets

Thomas F. Bloom, Jakob Führer, Oliver Roche-Newton

This paper considers some different measures for how additively structured a convex set can be. The main result gives a construction of a convex set $A$ containing $Ω (∣ A ∣^{3/2})$ t…

math.NT2023★ 4 cited

An improvement to the Kelley-Meka bounds on three-term arithmetic progressions

Thomas F. Bloom, Olof Sisask

In a recent breakthrough Kelley and Meka proved a quasipolynomial upper bound for the density of sets of integers without non-trivial three-term arithmetic progressions. We present…