Redmond McNamara

activity

20192026

collaborators

4 papers

math.DS2026

Monochromatic Almost-Pythagorean Quadruples

James Leng, Redmond McNamara, Andreas Mountakis

We prove that for any set $A$ with positive multiplicative upper density, there exist $x$ , $y$ , $z$ and $w$ in $A$ such that $x^{2} + y^{2} w^{2} = z^{2}$ , generalizing a result of Frantzik…

math.CO2023

A counterexample to Hildebrand's conjecture on stable sets

Redmond McNamara

We provide a counterexample to a conjecture of Hildebrand which states that if $§$ has positive lower density and is stable i.e. for all $d$ , $n$ is in $S$ if and only if…

math.NT2020

A Dynamical Proof of the Prime Number Theorem

Redmond McNamara

We present a new, elementary, dynamical proof of the prime number theorem.

math.DS2019

Sarnak's Conjecture for Sequences of Almost Quadratic Word Growth

Redmond McNamara

We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patter…