66 citations · 183 across the 33 of their papers we have counts for
36 papers
Unit fractions with shifted prime denominators
Thomas F. Bloom
We prove that any positive rational number is the sum of distinct unit fractions with denominators in . The same conclusion holds for the set $\{p-h : p…
The Kelley--Meka bounds for sets free of three-term arithmetic progressions
Thomas F. Bloom, Olof Sisask
We give a self-contained exposition of the recent remarkable result of Kelley and Meka: if has no non-trivial three-term arithmetic progressions then $\…
Asymptotic Approximate Fekete Arrays
T. Bloom, L. Bos, N. Levenberg
The notion of asymptotic Fekete arrays, arrays of points in a compact set which behave asymptotically like Fekete arrays, has been well-studied, albeit much mo…
On a density conjecture about unit fractions
Thomas F. Bloom
We prove that any set of positive upper density contains a finite such that , answering a question of Erdős and Graha…
A new upper bound for sets with no square differences
Thomas F. Bloom, James Maynard
We show that if has no solutions to with and then \[|A|\ll \frac{N}{(\log N)^{c\log\log \log N}}\] for some absolute consta…
Quantitative inverse theory of Gowers uniformity norms
Thomas F. Bloom
(This text is a survey written for the Bourbaki seminar on the work of F. Manners.) Gowers uniformity norms are the central objects of higher order Fourier analysis, one of the cor…