October 16, 2025Open Access

A note on monogenic even polynomials

Key Points

A conjecture by Lenny Jones is proved, categorizing even sextic monogenic polynomials effectively.
The study provides significant insights into the existence of infinite families of specific even sextic monogenic polynomials.
Connections to more general even polynomials, including power-compositional forms, are established as noteworthy.
Cyclic Galois groups are shown to play a crucial role in the classification of these polynomial types.

Abstract

We extend several predecessor works on even sextic monogenic polynomials. In particular, we prove a conjecture of Lenny Jones, thereby classifying even sextic monogenic polynomials with cyclic Galois group. This result is key to completing previous partial results on existence or non-existence of infinite families of even sextic monogenic polynomials with a prescribed Galois group. Some of the underlying ideas are relevant for investigation of more general families of even polynomials f (X²), or power-compositional polynomials f (X^).

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Cite This Study

Joachim König (Thu,) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd2e9 https://doi.org/https://doi.org/10.48550/arxiv.2505.10119

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