Michael T. Lacey

collaborators

4 papers

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.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.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.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…