Michael T. Lacey

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20232026

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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.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.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​

Szemerédi's Theorem Along Cantor Sets of Integers

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 $F_{p}^{n}$