On parameters of orders of quartic fields and essential pairs --\n extended version

2019/11/27 by Samuel A. Hambleton, Hambleton, Samuel A., Randy Yee +1
Computer Science · Mathematics · #11R04 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1911.12453

openalex publication_date 2019/11/27 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Classes of pairs of ternary quadratic forms parametrize quartic rings by a\nresult of Bhargava. We give an algorithm for finding a pair of ternary\nquadratic forms that parametrize a given order of a quartic field. We examine a\nnew technique, essential pairs, for obtaining parameters of orders of quartic\nfields from a number field database. Essential pairs for maximal orders of\nquartic fields are very common and provide a simple means of obtaining an\nintegral basis for the ring of integers.\n

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