Matt Hohertz

most citedCollatz polynomials: an introduction with bounds on their zeros

2 citations · 2 across the 4 of their papers we have counts for

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math.CV2021

An extension of the Geometric Modulus Principle to holomorphic and harmonic functions

Matt Hohertz

Kalantari's Geometric Modulus Principle describes the local behavior of the modulus of a polynomial. Specifically, if $p(z) = a_0 + \sum_{j=k}^n a_j\left(z-z_0\right)^j,\;a_0a_ka_n…

math.CV2020

A constructive proof of the convergence of Kalantari's bound on polynomial zeros

Matt Hohertz

In his 2006 paper, Jin proves that Kalantari's bounds on polynomial zeros, indexed by $m \leq 2$ and called $L_{m}$ and $U_{m}$ respectively, become sharp as $m \to \infty$ . That…

math.CV2020

Bounds for zeros of Collatz polynomials, with necessary and sufficient strictness conditions

Matt Hohertz

In a previous paper, we introduced the Collatz polynomials $P_{N} (z)$ , whose coefficients are the terms of the Collatz sequence of the positive integer $N$ . Our work in this paper ex…