Robert Fraser

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20172021

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math.CA2020

Three-term arithmetic progressions in subsets of $F_{q}^{\infty}$ of large Fourier dimension

Robert Fraser

We show that subsets of $F_{q}^{\infty}$ of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subs…

math.CA2019

On The Local Sum Conjecture in Two Dimensions

Robert Fraser, James Wright

In this paper we give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all…

math.CA2019

Polynomial Roth theorems on sets of fractional dimensions

Robert Fraser, Shaoming Guo, Malabika Pramanik

Let $E \subset R$ be a closed set of Hausdorff dimension $α \in (0, 1)$ . Let $P : R \to R$ be a polynomial without a constant term whose degree is bigger tha…

math.CA2018

A framework for constructing sets without configurations

Robert Fraser

We discuss a framework for constructing large subsets of $R^{n}$ and $K^{n}$ for non-archimedean local fields $K$ . This framework is applied to obtain new estimates for the Ha…

math.CA2017

Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the $p$ -adic numbers

Robert Fraser, Kyle Hambrook

We exhibit the first explicit examples of Salem sets in $Q_{p}$ of every dimension $0 < α < 1$ by showing that certain sets of well-approximable $p$ -adic numbers are Salem se…

Three-term arithmetic progressions in subsets of Fq∞​ of large Fourier dimension

On The Local Sum Conjecture in Two Dimensions

Polynomial Roth theorems on sets of fractional dimensions

A framework for constructing sets without configurations

Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the p-adic numbers

Three-term arithmetic progressions in subsets of $F_{q}^{\infty}$ of large Fourier dimension

Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in the $p$ -adic numbers