Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-06-03T08:53:29.065Z Has data issue: false hasContentIssue false

Use of the rabinowitsch polynomial to determine the class groups of a real quadratic field

Published online by Cambridge University Press:  17 April 2009

R.A. Mollin
Affiliation:
Department of Mathematics and StatisticsUniversity of CalgaryCalgary, Alberta T2N 1N4Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main result is a necessary and sufficient condition for the class group of a real quadratic field to be determined by primality properties of the well-known Rabinowitsch polynomial.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Dubois, E. and Levesque, C., ‘On determining certain real quadratic fields with class number one and relating this property to continued fractions and primality properties’, Nagoya Math. J. 124 (1991), 157180.CrossRefGoogle Scholar
[2]Hendy, M.D., ‘Applications of a continued fraction algorithm to some class number problems’, Math. Comp. 28 (1974), 267277.CrossRefGoogle Scholar
[3]Louboutin, S., ‘Continued fractions and real quadratic fields’, J. Number Theory 30 (1988), 167176.CrossRefGoogle Scholar
[5]Louboutin, S., Mollin, R.A. and Williams, H.C., ‘Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials, and quadratic residue covers’, Canad. J. Math. 44 (1992), 824842.CrossRefGoogle Scholar
[5]Lu, H., ‘On the class number of real quadratic fields’, Sci-Sinica (special issue (II)) (1979), 118130.Google Scholar
[6]Mollin, R.A., ‘An efficient method for the determination of certain real quadratic fields of class number one’, Utilitas Math. 40 (1991), 2732.Google Scholar
[7]Mollin, R.A., ‘The palindromic index – a measure of ambiguous classes with no ambiguous ideals in class groups of real quadratic orders’, Sém. Théor. Nombres Bordeaux (to appear).Google Scholar
[8]Williams, H.C. and Wunderlich, M.C., ‘On the parallel generation of the residues for the continued fraction factoring algorithm’, Math. Comp. 177 (1987), 405423.CrossRefGoogle Scholar