Michael T. Lacey

activity

20232026

collaborators

8 papers

math.NT2026

Density Bounds in Hua's Theorem for Prime Squares

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

We prove a density version of Hua's theorem in the five-variable case: if $P$ is a subset of the primes with relative lower density greater than $0.82$ , then every suffici…

math.NT2026

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

Alex Burgin, Anastasios Fragkos, David Kruzel +2

Given an integer $k \geq 2$ and a prime $p$ large enough depending on $k$ , we show that, if $A \subseteq F_{p}^{n}$ does not contain a restricted polynomial progression of the…

math.CA2026

Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

Anastasios Fragkos, Ben Krause, Michael Lacey

We study the near $L^{1}$ behavior of the maximally quadratically modulated Hilbert transform \[ \mathcal{C}_2f(x) := \sup_λ \left|\operatorname{p.v.} \int_{\mathbb{R}}f(x-y)e^{2 πi…

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…

math.DS2026

The Wiener Wintner Theorem Along the Primes

Jan Fornal, Anastasios Fragkos, Ben Krause +3

We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability sp…

math.NT2024

A Density Theorem for Higher Order Sums of Prime Numbers

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi +1

Let $P$ be a subset of the primes of lower density strictly larger than $\frac{1}{2}$ . Then, every sufficiently large even integer is a sum of four primes from the set $P$ . We establis…

math.NT2023

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

Christina Giannitsi, Ben Krause, Michael Lacey +2

We prove versions of Goldbach conjectures for Gaussian primes in arbitrary sectors. Fix an interval $ω \subset T$ . There is an integer $N_{ω}$ , so that every odd integer $n$ …

Density Bounds in Hua's Theorem for Prime Squares

Reasonable bounds for Restricted Polynomial Progressions in Fpn​

Endpoint Estimates for Stein's Purely Quadratic Carleson Operator

Szemerédi's Theorem Along Cantor Sets of Integers

Integer Cantor Sets: Arithmetic Combinatorial Properties

The Wiener Wintner Theorem Along the Primes

A Density Theorem for Higher Order Sums of Prime Numbers

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

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