B. Mance

activity

20092026

most citedCantor series constructions of sets of normal numbers

6 citations · 24 across the 22 of their papers we have counts for

collaborators

Showing 2013Show all

3 papers · 1 filter

math.NT2013

Number theoretic applications of a class of Cantor series fractal functions, II

Brian Li, Bill Mance

It is well known that all numbers that are normal of order $k$ in base $b$ are also normal of all orders less than $k$ . Another basic fact is that every real number is normal in ba…

math.NT2013

Number theoretic applications of a class of Cantor series fractal functions,I

Bill Mance

Suppose that $(P, Q) \in N_{2}^{N} \times N_{2}^{N}$ and $x = E_{0} . E_{1} E_{2} \dots$ is the $P$ -Cantor series expansion of $x \in R$ . We define $ψ_…

math.NT2013

On the Hausdorff dimension of countable intersections of certain sets of normal numbers

Bill Mance

We show that the set of numbers that are $Q$ -distribution normal but not simply $Q$ -ratio normal has full Hausdorff dimension. It is further shown under some conditions that counta…