1 citations · 2 across the 7 of their papers we have counts for
12 papers · 1 filter
Generalised Rado and Roth criteria
Jonathan Chapman, Sam Chow
We study the Ramsey properties of equations , where are integers, and is an integer polynomial of degree . Provided th…
A note on dyadic approximation in Cantor's set
Demi Allen, Simon Baker, Sam Chow +1
We consider the convergence theory for dyadic approximation in the middle-third Cantor set, , for approximation functions of the form (). In particular…
Counting multiplicative approximations
Sam Chow, Niclas Technau
A famous conjecture of Littlewood (c. 1930) concerns approximating two real numbers by rationals of the same denominator, multiplying the errors. In a lesser-known paper, Wang and…
Fully Inhomogeneous Multiplicative Diophantine Approximation of Badly Approximable Numbers
Sam Chow, Agamemnon Zafeiropoulos
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove…
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…
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…