R.A. Mollin, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4; email: ramollin@math.ucalgary.ca

Abstract/Résumé:

Central norms are given definition according to the infrastructure of the underlying order under discussion, which we define in the introductory section below. We relate these central norms in the simple continued fraction expansion of \(\sqrt{D}\) to solutions of the Eisenstein equation \(x^2-Dy^2 = -4\), with \(\gcd(x,y) = 1\). This provides a criterion for central norms to be \(4\) in the presence of certain congruence conditions on the fundamental unit of the underlying real quadratic order \(\mathbb{Z}[\sqrt{D}]\).

Keywords: Eisenstein equations, central norms, continued fractions

AMS Subject Classification: Quadratic and bilinear equations 11D09

PDF(click to download): Eisenstein Equations and Central Norms

R.A. Mollin

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: infrastructure of real quadratic fields, quadratic Diophantine equations, simple continued fractions

AMS Subject Classification: Continued fractions, Quadratic and bilinear equations, Quadratic extensions 11A55, 11D09, 11R11

PDF(click to download): When the Central Norm Equals 2 in the Simple Continued Fraction Expansion of a Quadratic Surd

T. Bülow

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Quadratic and bilinear equations 11D09

PDF(click to download): The Negative Pell Equation

R.A. Mollin

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Diophantine equations, continued fractions, ideals

AMS Subject Classification: Factorization; primality, Continued fractions, Quadratic and bilinear equations, Quadratic extensions 11A51, 11A55, 11D09, 11R11

PDF(click to download): Proof of Some Conjectures by Kaplansky