Simon Baker

collaborators

4 papers

math.NT2025

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 $I^¨ : (0, \infty) \to (0, \infty)$ and $I ¨ : (0, \infty) \to (0, 1)$ satisfying $\lim_{q\to\…

math.DS2025

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 \[ Î¼_Ï= \mathop{\circledast}_{k=1}^{\infty} \left( \frac{Î´_0 + Î´_{Î…

math.DS2025

On finitely many base $q$ expansions

Simon Baker, George Bender

Given some integer $m \geq 3$ , we find the first explicit collection of countably many intervals in $(1, 2)$ such that for any $q$ in one of these intervals, the set of points with…

math.DS2024

Fourier Decay from $L^{2}$ -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…

A quantitative framework for sets of exact approximation order by rational numbers

On the Fourier transform of random Bernoulli convolutions

On finitely many base q expansions

Fourier Decay from L2-Flattening

On finitely many base $q$ expansions

Fourier Decay from $L^{2}$ -Flattening