Kevin G. Hare

activity

20032023

most citedOn univoque Pisot numbers

20 citations · 128 across the 39 of their papers we have counts for

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16 papers · 1 filter

math.NT2023

Computational progress on the unfair 0-1 polynomial Conjecture

Kevin G. Hare

Let $c (x)$ be a monic integer polynomial with coefficients $0$ or $1$ . Write $c (x) = a (x) b (x)$ where $a (x)$ and $b (x)$ are monic polynomials with non-negative real (not necessaril…

math.NT2021★ 1 cited

Non-expansive matrix number systems with bases similar to $J_{n} (1)$

Joshua W. Caldwell, Kevin G. Hare, Tomáš Vávra

We study representations of integral vectors in a number system with a matrix base $M$ and vector digits. We focus on the case when $M$ is similar to $J_{n}$ , the Jordan block of $1$ …

math.NT2020★ 6 cited

Conjugates of Pisot numbers

Kevin G. Hare, Nikita Sidorov

In this paper we investigate the Galois conjugates of a Pisot number $q \in (m, m + 1)$ , $m \geq 1$ . In particular, we conjecture that for $q \in (1, 2)$ we have $|q'| \geq \frac{\sqr…

math.NT2019

On Newman and Littlewood polynomials with prescribed number of zeros inside the unit disk

Kevin G. Hare, Jonas Jankauskas

We study ${0, 1}$ and ${- 1, 1}$ polynomials $f (z)$ , called Newman and Littlewood polynomials, that have a prescribed number $N (f)$ of zeros in the open unit disk $\mathcal{D} =…

math.NT2019

Generalised Fibonacci sequences constructed from balancing words

Kevin Hare, J. C. Saunders

We study growth rates of generalised Fibonacci sequences of a particular structure. These sequences are constructed from choosing two real numbers for the first two terms and alway…

math.NT2016

On (a,b) Pairs in Random Fibonacci Sequences

Kevin G. Hare, J. C. Saunders

We study the random Fibonacci tree, which is an infinite binary tree with non-negative integers at each node. The root consists of the number 1 with a single child, also the number…