Lenny Jones

activity

20242026

collaborators

10 papers

math.NT2026

Characterizing monogenic trinomials $x^{12} + a x^{6} + b$ according to their Galois groups

Lenny Jones

Let $f (x) = x^{12} + a x^{6} + b \in Z [x]$ , with $ab \neq = 0$ . We say that $f (x)$ is {\em monogenic} if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, \dots, θ^{11}}$ is a…

math.NT2026

On the monogenicity and Galois groups of $x^{2 p} + a x^{p} + b^{p}$

Joshua Harrington, Lenny Jones

Let $f (x) = x^{2 p} + a x^{p} + b^{p}$ , where $p$ is a prime and $a, b \in Z$ with $ab \neq = 0$ . If $f (x)$ is irreducible over $Q$ , we say that $f (x)$ is monogenic if $\{1,θ,θ^2…

math.NT2026

Monogenic even sextic trinomials and their Galois groups

Lenny Jones

Let $f (x) = x^{6} + A x^{2 k} + B \in Z [x]$ , with $A \neq = 0$ and $k \in {1, 2}$ . We say that $f (x)$ is {\em monogenic} if $f (x)$ is irreducible over $Q$ and $\{1,θ,θ^2,θ^3,θ…

math.NT2025

Monogenic Strictly-Perron Polynomials

Lenny Jones

A monic polynomial $f (x) \in Z [x]$ of degree $n$ is called monogenic if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, \dots, θ^{n - 1}}$ is a basis for the ring…

math.NT2025

Monogenic sextic trinomials $x^{6} + A x^{3} + B$ and their Galois groups

Joshua Harrington, Lenny Jones

Let $f (x) = x^{6} + A x^{3} + B \in Z [x]$ , with $A \neq = 0$ , and suppose that $f (x)$ is irreducible over $Q$ . We define $f (x)$ to be {\em monogenic} if $\{1,θ,θ^2,θ^3,θ^4,θ^{5…

math.NT2025

Monogenic Reciprocal Quartic Polynomials And Their Galois Groups

Lenny Jones

Suppose that $f (x) = x^{4} + A x^{3} + B x^{2} + A x + 1 \in Z [x]$ . We say that $f (x)$ is monogenic if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, θ^{3}}$ is a basis for the ring…

Characterizing monogenic trinomials x12+ax6+b according to their Galois groups

On the monogenicity and Galois groups of x2p+axp+bp

Monogenic even sextic trinomials and their Galois groups

Monogenic Strictly-Perron Polynomials

Monogenic sextic trinomials x6+Ax3+B and their Galois groups

Monogenic Reciprocal Quartic Polynomials And Their Galois Groups

Characterizing monogenic trinomials $x^{12} + a x^{6} + b$ according to their Galois groups

On the monogenicity and Galois groups of $x^{2 p} + a x^{p} + b^{p}$

Monogenic sextic trinomials $x^{6} + A x^{3} + B$ and their Galois groups