B. Mance

collaborators

4 papers

math.NT2026

Discretized Rotation with fixed initial points

Shigeki Akiyama, Bill Mance

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

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 $x_{n} = I^¾_{1} I^\pm_{1}^{n} + I^¾_{2} I^\pm_{2}^{n}$ ( $n = 0, 1, \dots$ ) with companion polynomial $P (X)$ . For example, the sequence $x_n=Î¾_1(4+\sqrt{2})^n+Î…

math.LO2025

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…