Michael T. Lacey

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math.NT2026

SzemerÃ©di'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…