2024/05/30 by Paul Voutier, Voutier, Paul M.
Mathematics · #11R16 11R32 #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2405.20288
openalex publication_date 2024/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.