3 citations · 4 across the 7 of their papers we have counts for
8 papers
Twin primes and the -sphere
Samuel A. Hambleton
We investigate the group of points of the -sphere modulo a prime, point out connections to other known groups and the Chebyshev polynomials, and show that there is an infinite s…
On parameters of orders of quartic fields and essential pairs -- extended version
Samuel A. Hambleton, Randy Yee
Classes of pairs of ternary quadratic forms parametrize quartic rings by a result of Bhargava. We give an algorithm for finding a pair of ternary quadratic forms that parametrize a…
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…
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…
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…
Arithmetic of Pell surfaces
Samuel Hambleton, Franz Lemmermeyer
We define a group stucture on the primitive integer points (A,B,C) of the algebraic variety Q_0(B,C)=A^n, where Q_0 is the principal binary quadratic form of fundamental discrimina…
An isomorphism between the narrow ideal class group of squared ideals of a quadratic number field and the kernel of a homomorphism between cohomology groups for Pell conics
Samuel A. Hambleton
Two proofs are provided that the narrow ideal class group of squared ideals of a quadratic number field is isomorphic to the kernel of a homomorphism between cohomology groups for…
A binomial identity on the least prime factor of an integer
Samuel A. Hambleton
An identity for binomial symbols modulo an odd positive integer relating to the least prime factor of is proved. The identity is discussed within the context of Pell conics…