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math.NT2018★ 3 cited
Arithmetic matrices for number fields I
Samuel A. Hambleton
We provide a simple way to add, multiply, invert, and take traces and norms of algebraic integers of a number field using integral matrices. With formulas for the integral bases of…
math.NT2018★ 1 cited
Arithmetic matrices for number fields II: Parametrization of rings by binary forms
Samuel A. Hambleton
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 re…
math.NT2018
A cubic generalization of Brahmagupta's identity
Samuel A. Hambleton
We give an algebraic identity for cubic polynomials which generalizes Brahmagupta's identity and facilitates arithmetic in cubic fields. We also pose a question about a relationshi…