S. Baker

activity

20122023

most citedUnique expansions and intersections of Cantor sets

10 citations · 77 across the 32 of their papers we have counts for

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18 papers · 1 filter

math.NT2022★ 1 cited

Approximating elements of the middle third Cantor set with dyadic rationals

Simon Baker

Let $C$ be the middle third Cantor set and $μ$ be the $\frac{l o g 2}{l o g 3}$ -dimensional Hausdorff measure restricted to $C$ . In this paper we study approximations of elements of…

math.NT2022

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, $K$ , for approximation functions of the form $ψ_{τ} (n) = n^{- τ}$ ( $τ \geq 0$ ). In particular…

math.NT2021

Metric results for numbers with multiple $q$ -expansions

Simon Baker, Yuru Zou

Let $M$ be a positive integer and $q \in (1, M + 1]$ . A $q$ -expansion of a real number $x$ is a sequence $(c_{i}) = c_{1} c_{2} \dots$ with $c_{i} \in {0, 1, \dots, M}$ such that $x=\sum_{i=1}^{…

math.NT2021

Intrinsic Diophantine Approximation for overlapping iterated function systems

Simon Baker

In this paper we study a family of limsup sets that are defined using iterated function systems. Our main result is an analogue of Khintchine's theorem for these sets. We then appl…

math.NT2020★ 6 cited

Gap statistics and higher correlations for geometric progressions modulo one

Christoph Aistleitner, Simon Baker, Niclas Technau +1

Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every $α > 1$ , the fractional parts of the geometric progression $(α^{n})_{n \geq 1}$ are equidistributed mo…

math.NT2019

On the pair correlations of powers of real numbers

Christoph Aistleitner, Simon Baker

A classical theorem of Koksma states that for Lebesgue almost every $x > 1$ the sequence $(x^{n})_{n = 1}^{\infty}$ is uniformly distributed modulo one. In the present paper we extend Ko…