Alex Burgin

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2026

Reasonable bounds for Restricted Polynomial Progressions in $F_{p}^{n}$

Alex Burgin, Anastasios Fragkos, David Kruzel +2

Given an integer $k \geq 2$ , there are integers $M_{k}$ and $P_{k}$ so that for all $A \subseteq F_{p}^{n}$ does not contain a restricted polynomial progression of the form \begin{…

math.NT2026

Remarks on the Geometry of Sets in $Z^{d}$ with Small Fourier $L^{1}$ Norm

Alex Burgin, Junzhe Mao

We study geometric inverse problems for finite sets $A \subset Z^{d}$ whose Fourier $L^{1}$ norm, or Wiener norm, \begin{align*} \|A\|:=\int_{\mathbb{T}^d}\Big|\sum_{a\in A}e(a…

math.NT2026

Szemerédi's Theorem Along Cantor Sets of Integers

Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2

Let $C = {k_{1} < k_{2} < \dots}$ be Cantor set of integers, that is a set of integers with restricted digits modulo a base $b$ , and suppose $0$ is one of the restricted digit…

Reasonable bounds for Restricted Polynomial Progressions in Fpn​

Remarks on the Geometry of Sets in Zd with Small Fourier L1 Norm

Szemerédi's Theorem Along Cantor Sets of Integers

Reasonable bounds for Restricted Polynomial Progressions in $F_{p}^{n}$

Remarks on the Geometry of Sets in $Z^{d}$ with Small Fourier $L^{1}$ Norm