continued fractions — 4 articles found.

Eisenstein Equations and Central Norms

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 20–24
Vol.27 (1) 2005
R.A. Mollin Details
(Received: 2004-06-14 )
(Received: 2004-06-14 )

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

C. R. Math. Rep. Acad. Sci. Canada Vol. 24 (3) 2002, pp. 102–108
Vol.24 (3) 2002
R.A. Mollin Details
(Received: 2001-11-20 )
(Received: 2001-11-20 )

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

C. R. Math. Rep. Acad. Sci. Canada Vol. 23 (2) 2001, pp. 60–64
Vol.23 (2) 2001
R.A. Mollin Details
(Received: 2000-10-27 )
(Received: 2000-10-27 )

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

C. R. Math. Rep. Acad. Sci. Canada Vol. 17 (4) 1995, pp. 170–174
Vol.17 (4) 1995
R.A. Mollin Details
(Received: 1995-08-11 )
(Received: 1995-08-11 )

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