continued fractions — 4 articles found.
Eisenstein Equations and Central Norms
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
Continued fractions beepers and Fibonacci numbers
R.A. Mollin
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords: Fibonacci numbers, continued fractions, fundamental units, period length
AMS Subject Classification:
Continued fractions,
11A55, 11Rl l
PDF(click to download): Continued fractions beepers and Fibonacci numbers
Proof of Some Conjectures by Kaplansky
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
The number of ambiguous cycles of reduced ideals
R.A. Mollin
Abstract/Résumé:
No abstract available but the full text pdf may be downloaded at the title link below.
Keywords: ambiguous cycle, continued fractions, real quadratic order, sums of squares
AMS Subject Classification:
Quadratic extensions, Class numbers; class groups; discriminants, Class groups and Picard groups of orders
11R11, 11R29, 11R65
PDF(click to download): The number of ambiguous cycles of reduced ideals