6 papers · 1 filter
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 is a subset of the primes with relative lower density greater than , then every suffici…
Reasonable bounds for Restricted Polynomial Progressions in
Alex Burgin, Anastasios Fragkos, David Kruzel +2
Given an integer and a prime large enough depending on , we show that, if does not contain a restricted polynomial progression of the…
Endpoint Estimates for Stein's Purely Quadratic Carleson Operator
Anastasios Fragkos, Ben Krause, Michael Lacey
We study the near 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…
Szemerédi's Theorem Along Cantor Sets of Integers
Alex Burgin, Anastasios Fragkos, Michael T. Lacey +2
Let be Cantor set of integers, that is a set of integers with restricted digits modulo a base , and suppose is one of the restricted digit…
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…
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…