Families of cyclic quartic monogenic polynomials
Volume 219 / 2025
Acta Arithmetica 219 (2025), 365-377
MSC: Primary 11R16; Secondary 11R32
DOI: 10.4064/aa240919-10-3
Published online: 23 June 2025
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.
