4 citations · 5 across the 9 of their papers we have counts for
10 papers
Remarks on the inverse Littlewood conjecture
Thomas F. Bloom, Ben Green
The Littlewood conjecture, proven by Konyagin and McGehee-Pigno-Smith in the 1980s, states that if is a finite set of integers with then $\…
More on the sum-product problem for integers with few prime factors
Rishika Agrawal, Thomas F. Bloom, Giorgis Petridis
We show that if is a finite set of integers in which every integer is divisible by many primes then \[\max(\lvert A+A\rvert,\lvert AA\rvert) \geq \lver…
Integers with small digits in multiple bases
Thomas F. Bloom, Ernie Croot
We show that, for any , if are distinct coprime integers, sufficiently large depending only on , then for any there are infinitely many integers…
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 containing t…
Control and its applications in additive combinatorics
Thomas F. Bloom
We prove new quantitative bounds on the additive structure of sets obeying an 'control' assumption, which arises naturally in several questions within additive combinatorics.…
A polynomial Freiman-Ruzsa inverse theorem for function fields
Thomas F. Bloom
Using the recent proof of the polynomial Freiman-Ruzsa conjecture over by Gowers, Green, Manners, and Tao, we prove a version of the polynomial Freiman-Ruzsa conje…
The Bombieri-Pila determinant method
Thomas F. Bloom, Jared Duker Lichtman
We give a concise and accessible introduction to the real-analytic determinant method for counting integral points on algebraic curves, based on the classic 1989 paper of Bombieri…
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…
Egyptian Fractions
Thomas F. Bloom, Christian Elsholtz
Any rational number can be written as the sum of distinct unit fractions. In this survey paper we review some of the many interesting questions concerning such 'Egyptian fraction'…
Ramsey equivalence of and
Thomas F. Bloom, Anita Liebenau
We prove that, for , the graphs and are Ramsey equivalent. That is, if is such that any red-blue colouring of its edges creates a monochromatic $K_…