Alex Burgin

collaborators

4 papers

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.DS2026

Ergodic Averages over Shrinking Sectors of $Z [i]$

Alex Burgin, Christina Giannitsi

We study ergodic averages over Gaussian integers in shrinking angular sectors, which impose an increasingly restrictive directional relation between the real and imaginary coordina…

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…

math.DS2026

Integer Cantor Sets: Arithmetic Combinatorial Properties

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

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we…

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

Ergodic Averages over Shrinking Sectors of Z[i]

Szemerédi's Theorem Along Cantor Sets of Integers

Integer Cantor Sets: Arithmetic Combinatorial Properties

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

Ergodic Averages over Shrinking Sectors of $Z [i]$