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arXiv · 2405.20288

A family of cyclic quartic monogenic polynomials

Paul M. Voutier
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Abstract

We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $abc$ conjecture holds, generate distinct monogenic quartic fields infinitely often. Additional families (also conjecturally generating infinitely many distinct fields) are provided in Section 4, including what appears to be an infinite collection of such families.

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Paul M. Voutier. 2024-05-30. A family of cyclic quartic monogenic polynomials. https://doi.org/10.4064/aa240919-10-3

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