Arithmetic matrices for number fields II: Parametrization of rings by binary forms

2018/08/30 by Samuel A. Hambleton, Hambleton, Samuel A.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.10214

openalex publication_date 2018/08/30 · openalex created_date 2018/09/07 · openalex updated_date 2026/07/28

Abstract

We show that binary forms of degree n less than seven parameterize rings, generalizing a result of Levi on binary cubic forms parameterizing cubic rings, which can be related to results of Bhargava. The question of whether or not a binary form of degree n parameterizes a ring of rank n depends on a symbolic calculation with matrices.

Cited by

• Arithmetic matrices for number fields I

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