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papers

Publications (45)

math.NT2020

On Fibonacci partitions

Sam Chow, Tom Slattery

We prove an exact formula for OEIS A000119, which counts partitions into distinct Fibonacci numbers. We also establish an exact formula for its mean value, and determine the asympt…

math.NT2018

Additive energy and the metric Poissonian property

Thomas F. Bloom, Sam Chow, Ayla Gafni +1

Let $A$ be a set of natural numbers. Recent work has suggested a strong link between the additive energy of $A$ (the number of solutions to $a_{1} + a_{2} = a_{3} + a_{4}$ with $a_{i} \in A$ …

math.NT2026

Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds

Sam Chow, Rajula Srivastava, Niclas Technau +1

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subs…

math.NT2017

Bohr sets and multiplicative diophantine approximation

Sam Chow

In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of G…

math.NT2020

Dyadic Approximation in the Middle-Third Cantor Set

Demi Allen, Sam Chow, Han Yu

In this paper, we study the metric theory of dyadic approximation in the middle-third Cantor set. This theory complements earlier work of Levesley, Salp, and Velani (2007), who inv…

math.NT2025

Twisted Diophantine approximation for matrix transformations of tori

Sam Chow, Qing-Long Zhou

Consider a sequence of integral matrices $A = (A_{n})_{n \in N}$ , and a $d$ -tuple function $r = (r_{1}, \dots, r_{d}) : N \to (0, \frac{1}{2})$ . For a fixed vector ${\bm Î±}…