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2020 Generating Infinite Families of Monogenic Polynomials Using a New Discriminant Formula
Lenny Jones
Author Affiliations +
Albanian J. Math. 14(1): 37-45 (2020). DOI: 10.51286/albjm/1608313765

Abstract

Recently, Otake and Shaska have given a formula for the discriminant of quadrinomials of the form $f(x) = x^n + t(x^2 + ax + b)$. In their concluding remarks, they ask if a formula can be found for the discriminant of $f(x) = x^n + tg(x)$ when $n > \deg(g) = 3$. Assuming that $f(x) = x^n + tg(x)$ is irreducible, and under certain restrictions on a polynomial related to $g(x)$, in this article we give a formula for the discriminant of $f(x)$, regardless of $\deg(g) \ge 1$. We then use our discriminant formula to generate some new infinite families of monogenic polynomials $f(x) = x^n + tg(x)$ with $n > \deg(g)$, when $g(x)$ is monic and $\deg(g)\in 2 \{2, 3, 4\}$.

Citation

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Lenny Jones. "Generating Infinite Families of Monogenic Polynomials Using a New Discriminant Formula." Albanian J. Math. 14 (1) 37 - 45, 2020. https://doi.org/10.51286/albjm/1608313765

Information

Published: 2020
First available in Project Euclid: 18 December 2020

zbMATH: 1441.11268
MathSciNet: MR4086717
Digital Object Identifier: 10.51286/albjm/1608313765

Subjects:
Primary: 11R04
Secondary: 11R09, 12F05

Rights: Copyright © 2020 Research Institute of Science and Technology (RISAT)

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Vol.14 • No. 1 • 2020
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