Publications:
S. A. Hambleton, H. C. Williams, Cubic Fields with Geometry, CMS Books in Mathematics, Springer, 2018. (Also see errata and summary by Daniel C. Mayer)
______________, A cubic generalization of Brahmagupta's identity, Journal of the Ramanujan Math. Soc., 32, 4, (2017), 327--337.
______________, Generalized Lucas-Lehmer tests using Pell conics, Proc. Amer. Math. Soc., 140, (2012), no. 8, 2653--2661.
______________, A brief summary of binary quadratic forms, Surveys in Mathematics and Mathematical Sciences, 1, (2012), no. 1, 65--80.
______________, V. Scharaschkin, Pell conics and quadratic reciprocity, Rocky Mountain J. Math., 42, (2012), no. 1, 91--96.
______________, F. Lemmermeyer, Arithmetic of Pell surfaces, Acta. Arith. 146, (2011), 1--12.
______________, V. Scharaschkin, Quadratic reciprocity via resultants, International Journal of Number Theory, 6, 6, (2010), 1413--1417.
ArXiv papers:
On parameters of orders of quartic fields and essential pairs -- extended version joint work with Randy Yee
Arithmetic matrices for number fields II: Parametrization of rings by binary forms
Arithmetic matrices for number fields I
A binomial identity on the least prime factor of an integer
Ph.D. Thesis :
Arithmetic of affine algebraic groups from norm forms in quadratic and cubic fields PhD Thesis, School of Mathematics & Physics, The University of Queensland. 2012.
Educational Notes :
Vortex-based mathematics is modular arithmetic
Continued fractions and Pell conics
Mathematics Quick Reference, also in print