46 citations · 268 across the 58 of their papers we have counts for
8 papers · 1 filter
Intermediate dimensions
Kenneth J. Falconer, Jonathan M. Fraser, Tom Kempton
We introduce a continuum of dimensions which are `intermediate' between the familiar Hausdorff and box dimensions. This is done by restricting the families of allowable covers in t…
Attainable values for the Assouad dimension of projections
Jonathan M. Fraser, Antti Käenmäki
We prove that for an arbitrary upper semi-continuous function there exists a compact set in the plane such that for all…
Almost arithmetic progressions in the primes and other large sets
Jonathan M. Fraser
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithmetic progressions. In this note I provide a straightforward argument demonstrati…
On the Hausdorff dimension of microsets
Jonathan M. Fraser, Douglas C. Howroyd, Antti Käenmäki +1
We investigate how the Hausdorff dimensions of microsets are related to the dimensions of the original set. It is known that the maximal dimension of a microset is the Assouad dime…
The dimensions of inhomogeneous self-affine sets
Stuart A. Burrell, Jonathan M. Fraser
We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In ad…
The Assouad spectrum of random self-affine carpets
Jonathan M. Fraser, Sascha Troscheit
We derive the almost sure Assouad spectrum and quasi-Assouad dimension of random self-affine Bedford-McMullen carpets. Previous work has revealed that the (related) Assouad dimensi…