25 citations · 27 across the 5 of their papers we have counts for
Showing math.NTShow all
3 papers · 1 filter
math.NT2026★ 1 cited
The sum-product conjecture is false for real numbers
Thomas F Bloom, Will Sawin, Carl Schildkraut +1
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…
math.NT2023
Odd moments and adding fractions
Thomas F. Bloom, Vivian Kuperberg
We prove near-optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an applicat…
math.NT2011★ 25 cited
Translation invariant equations and the method of Sanders
Thomas Bloom
We extend the recent improvement of Roth's theorem on three term arithmetic progressions by Sanders to obtain similar results for the problem of locating non-trivial solutions to t…