Thomas F. Bloom

activity

20152026

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

4 citations · 5 across the 9 of their papers we have counts for

collaborators

Showing 2025Show all

4 papers · 1 filter

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.NT2025

Control and its applications in additive combinatorics

Thomas F. Bloom

We prove new quantitative bounds on the additive structure of sets obeying an $L^{3}$ 'control' assumption, which arises naturally in several questions within additive combinatorics.…

math.NT2025

A polynomial Freiman-Ruzsa inverse theorem for function fields

Thomas F. Bloom

Using the recent proof of the polynomial Freiman-Ruzsa conjecture over $F_{p}^{n}$ by Gowers, Green, Manners, and Tao, we prove a version of the polynomial Freiman-Ruzsa conje…