2022/06/24 by David L. Pincus, Pincus, David L., Lawrence C. Washington +1
Computer Science · Mathematics · #11R29 #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2206.12313
openalex publication_date 2022/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We adapt a known technique for searching for ideal classes of arbitrary order and then apply it to three families of number fields. We show that a family of cyclic sextic number fields has infinitely many fields in it that contain a relative ideal class of order r, where r is a positive integer relatively prime to the degree of the extension. We then show that the same holds true for a family of cyclic quartic number fields. Though the technique is traditionally applied to Galois extensions, we show how it may be adapted to handle a family of non-Galois cubic number fields and prove that this family contains infinitely many fields with an ideal class of arbitrary order relatively prime to three.