Bounds for zeros of Collatz polynomials, with necessary and sufficient strictness conditions
| العنوان: | Bounds for zeros of Collatz polynomials, with necessary and sufficient strictness conditions |
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| المؤلفون: | Matt Hohertz |
| المصدر: | Complex Variables and Elliptic Equations. :1-7 |
| بيانات النشر: | Informa UK Limited, 2023. |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | Computational Mathematics, Numerical Analysis, Mathematics - Complex Variables, Applied Mathematics, FOS: Mathematics, 30C15 (primary), 30C10 (secondary), Complex Variables (math.CV), Analysis |
| الوصف: | 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 expands on our previous results, using the Enestr\"om-Kakeya Theorem to tighten our old bounds of the roots of $P_N(z)$ and giving precise conditions under which these new bounds are sharp. In particular, we confirm an experimental result that zeros on the circle $\{z\in\mathbb{C}: |z| = 2\}$ are rare: the set of $N$ such that $P_N(z)$ has a root of modulus 2 is sparse in the natural numbers. We close with some questions for further study. Comment: 8 pages, 1 figure |
| تدمد: | 1747-6941 1747-6933 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9e965e145c3cbfa582158f16f0110285Test https://doi.org/10.1080/17476933.2022.2142784Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....9e965e145c3cbfa582158f16f0110285 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 17476941 17476933 |
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