Redmond McNamara

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20192026

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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.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…