Christopher Lutsko

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math.NT2026

Poissonian correlations of $I^\pm n^{d}$ mod $1$

Chris Lutsko, Nick Rome, Niclas Technau

Let $x (n) := I^\pm n^{d} mod 1$ for integer $d > 1$ and non-zero real $I^\pm$ . We show that ${x (n)}_{n > 0}$ has Poissonian $ℓ$ -point correlations for almost all choices of $I^\pm$ when $d$ i…

math.NT2025

The Gauss circle problem for Penrose tilings

Alan Haynes, Christopher Lutsko

Let $B_{R}$ denote the closed Euclidean ball of radius $R$ in the plane. In this paper we prove that, if $V$ is the set of vertices of any unit length rhombic Penrose tiling then, fo…

Poissonian correlations of I^±nd mod 1

The Gauss circle problem for Penrose tilings

Poissonian correlations of $I^\pm n^{d}$ mod $1$