Kevin G. Hare

activity

20102024

most citedGrowth degree classification for finitely generated semigroups of integer matrices

4 citations · 8 across the 10 of their papers we have counts for

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7 papers · 1 filter

math.NT2023

Self-similar sets and self-similar measures in the $p$ -adics

Kevin G. Hare, Tomáš Vávra

In this paper we investigate $p$ -adic self-similar sets and $p$ -adic self-similar measures. We show that $p$ -adic self-similar sets are $p$ -adic path set fractals, and that the con…

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.NT2014★ 4 cited

Growth degree classification for finitely generated semigroups of integer matrices

Jason P. Bell, Michael Coons, Kevin G. Hare

Let $A$ be a finite set of $d \times d$ matrices with integer entries and let $m_{n} (A)$ be the maximum norm of a product of $n$ elements of $A$ . In this…

math.NT2014★ 1 cited

The minimal growth of a $k$ -regular sequence

Jason P. Bell, Michael Coons, Kevin G. Hare

We determine a lower gap property for the growth of an unbounded $\mathbb{Z}$-valued $k$-regular sequence. In particular, if $f:\mathbb{N}\to\mathbb{Z}$ is an unbounded $k$…

math.NT2014★ 2 cited

There are no two non-real conjugates of a Pisot number with the same imaginary part

Artūras Dubickas, Kevin G. Hare, Jonas Jankauskas

We show that the number $α = (1 + 3 + 25) /2$ with minimal polynomial $x^{4} - 2 x^{3} + x - 1$ is the only Pisot number whose four distinct conjugates $α_{1}, α_{2}, α_{3}, α_{4}$ satisfy the ad…

math.NT2010

The sum of digits of $n$ and $n^{2}$

K. G. Hare, S. Laishram, T. Stoll

Let $s_{q} (n)$ denote the sum of the digits in the $q$ -ary expansion of an integer $n$ . In 2005, Melfi examined the structure of $n$ such that $s_{2} (n) = s_{2} (n^{2})$ . We extend this stu…

Self-similar sets and self-similar measures in the p-adics