6 papers
A quantitative framework for sets of exact approximation order by rational numbers
Simon Baker, Benjamin Ward
In this paper we study a quantitative notion of exactness within Diophantine approximation. Given and satisfying $\lim_{q\to\in…
On the Fourier transform of random Bernoulli convolutions
Simon Baker, Henna Koivusalo, Sascha Troscheit +1
We investigate random Bernoulli convolutions, namely, probability measures given by the infinite convolution \[ μ_ω= \mathop{\circledast}_{k=1}^{\infty} \left( \frac{δ_0 + δ_{λ_1 λ…
On finitely many base expansions
Simon Baker, George Bender
Given some integer , we find the first explicit collection of countably many intervals in such that for any in one of these intervals, the set of points with…
Fourier Decay from -Flattening
Simon Baker, Osama Khalil, Tuomas Sahlsten
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the…
On the cardinality and dimension of the slices of Okamoto's functions
Simon Baker, George Bender
The graphs of Okamoto's functions, denoted by , are self-affine fractal curves contained in , parameterised by . In this paper we consider the cardinalit…
On normal numbers and self-similar measures
Amir Algom, Simon Baker, Pablo Shmerkin
Let be a self-similar IFS on and let be a Pisot number. We prove that if fo…