Christopher Lutsko

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20192026

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math.NT2026

Poissonian pair correlations for the three-particle Sutherland model

Christopher Lutsko

We prove a Berry-Tabor theorem for the repulsive three-particle trigonometric Sutherland Hamiltonian. For fixed total momentum, its relative spectrum is an affine translate of the…

math.NT2026

Poissonian correlations of $α n^{d}$ mod $1$

Chris Lutsko, Nick Rome, Niclas Technau

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

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…

math.NT2024

Average variance bounds for integer points on the sphere

Christopher Lutsko

Let $E (n)$ denote the set of integer points on the sphere $∣ x ∣^{2} = n$ , projected radially onto the unit sphere. Under the usual congruence conditions on $…

math.NT2024

Lax-Phillips orbit counting in higher rank

Alex Kontorovich, Christopher Lutsko

Given a discrete lattice, $Γ < SL_{m} (R)$ , and a base point $o \in R^{m}$ , let $N_{Γ} (T)$ denote the number of points in the orbit $o \cdot Γ$ whose (Eucl…

Poissonian pair correlations for the three-particle Sutherland model

Poissonian correlations of αnd mod 1

The Gauss circle problem for Penrose tilings

Average variance bounds for integer points on the sphere

Lax-Phillips orbit counting in higher rank

Poissonian correlations of $α n^{d}$ mod $1$