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Weighted approximation in higher-dimensional missing digit sets
Demi Allen, Benjamin Ward
In this note, we use the mass transference principle for rectangles, recently obtained by Wang and Wu (Math. Ann., 2021), to study the Hausdorff dimension of sets of "weighted -…
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…
Independence inheritance and Diophantine approximation for systems of linear forms
Demi Allen, Felipe A. Ramirez
The classical Khintchine-Groshev theorem is a generalization of Khintchine's theorem on simultaneous Diophantine approximation, from approximation of points in to app…
A note on weighted simultaneous Diophantine approximation on manifolds
Demi Allen, Baowei Wang
In this note, we present an improvement to a recent result due to Beresnevich, Levesley, and Ward (2021) pertaining to weighted simultaneous Diophantine approximation on manifolds.
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…
A General Mass Transference Principle
Demi Allen, Simon Baker
In this paper we prove a general form of the Mass Transference Principle for sets defined via neighbourhoods of sets satisfying a certain local scaling property. Such set…