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

32 papers

math.NT2026

On the Hausdorff dimension of the difference sets between typical and normal numbers

Bill Mance, Jakub Tomaszewski

We study the Hausdorff dimension of the difference sets between the set of typical numbers, defined via the Erdős--Rényi law governing the longest run of digits, and the set of num…

math.DS2025

The Theory of Normality for Dynamically Generated Cantor Series Expansions

Sohail Farhangi, Bill Mance

The theory of normality for base $g$ expansions of real numbers in $[0, 1)$ is rich and well developed. Similar theories have been developed for many other numeration systems, such…

math.LO2025

Borel Complexity of the set of vectors normal for a fixed recurrence sequence

Hajime Kaneko, Bill Mance

In this paper, we consider recurrence sequences $x_{n} = ξ_{1} α_{1}^{n} + ξ_{2} α_{2}^{n}$ ( $n = 0, 1, \dots$ ) with companion polynomial $P (X)$ . For example, the sequence $x_n=ξ_1(4+\sqrt{2})^n+ξ_2(4-…

math.NT2025

Discretized Rotation with fixed initial points

Shigeki Akiyama, Bill Mance

We prove that if $max {∣ a_{0} ∣, ∣ a_{1} ∣} \leq 10$ and $λ \in] - 2, 2 [$ , then the sequence defined by $0 \leq a_{n + 2} + λ a_{n + 1} + a_{n} < 1$ is periodic.

math.LO2024

Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem

Sohail Farhangi, Steve Jackson, Bill Mance

We show that several sets of interest arising from the study of partition regularity and density Ramsey theory of polynomial equations over integral domains are undecidable. In par…

math.LO2023

The descriptive complexity of the set of Poisson generic numbers

Verónica Becher, Stephen Jackson, Dominik Kwietniak +1

Let $b \geq 2$ be an integer. We show that the set of real numbers that are Poisson generic in base $b$ is $Π_{3}^{0}$ -complete in the Borel hierarchy of subsets of the real l…