T. Bloom

activity

20062023

most citedA quantitative improvement for Roth's theorem on arithmetic progressions

66 citations · 183 across the 33 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

math.CO2018★ 5 cited

Logarithmic bounds for Roth's theorem via almost-periodicity

Thomas F. Bloom, Olof Sisask

We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \subset {1, 2, \dots, N}$ is free of three-term progressions, then $\lver…

math.CV2018

Pluripotential Theory and Convex Bodies: Large Deviation Principle

Turgay Bayraktar, Thomas Bloom, Norman Levenberg +1

We continue the study in a previous work in the setting of weighted pluripotential theory arising from polynomials associated to a convex body $P$ in $(R^{+})^{d}$ . Our goal is t…

math.NT2018

GCD sums and sum-product estimates

Thomas F. Bloom, Aled Walker

In this note we prove a new estimate on so-called GCD sums (also called Gál sums), which, for certain coefficients, improves significantly over the general bound due to de la Bretè…

math.CV2018

The Extremal Function for the Complex Ball for Generalized Notions of Degree and Multivariate Polynomial Approximation

T. Bloom, L. Bos, N. Levenberg +2

We discuss the Siciak-Zaharjuta extremal function of pluripotential theory for the unit ball in C^d for spaces of polynomials with the notion of degree determined by a convex body…

math.PR2018

Asymptotic zero distribution of random orthogonal polynomials

Thomas Bloom, Duncan Dauvergne

We consider random polynomials of the form $H_{n} (z) = \sum_{j = 0}^{n} ξ_{j} q_{j} (z)$ where the ${ξ_{j}}$ are i.i.d non-degenerate complex random variables, and the ${q_{j} (z)}$ are orthonorma…