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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Showing 2014 · math.NTShow all

3 papers · 2 filters

math.NT2014★ 7 cited

On the distribution of powers of real numbers modulo 1

Simon Baker

Given a strictly increasing sequence of positive real numbers tending to infinity $(q_{n})_{n = 1}^{\infty}$ , and an arbitrary sequence of real numbers $(r_{n})_{n = 1}^{\infty} .$ We s…

math.NT2014

Approximation properties of $β$ -expansions

Simon Baker

Let $β \in (1, 2)$ and $x \in [0, \frac{1}{β - 1}]$ . We call a sequence $(ε_{i})_{i = 1}^{\infty} \in {0, 1}^{N}$ a $β$ -expansion for $x$ if $x = \sum_{i = 1}^{\infty} ε_{i} β^{- i}$ . We cal…

math.NT2014

Badly approximable numbers for sequences of balls

Simon Baker

It is a classical result from Diophantine approximation that the set of badly approximable numbers has Lebesgue measure zero. In this paper we generalise this result to more genera…

On the distribution of powers of real numbers modulo 1

Approximation properties of β-expansions

Badly approximable numbers for sequences of balls

Approximation properties of $β$ -expansions