The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders

Richard A. Mollin

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 2, page 447-460
  • ISSN: 1246-7405

Abstract

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Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.

How to cite

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Mollin, Richard A.. "The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders." Journal de théorie des nombres de Bordeaux 7.2 (1995): 447-460. <http://eudml.org/doc/247666>.

@article{Mollin1995,
abstract = {Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.},
author = {Mollin, Richard A.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {quadratic order; class number; palindromic index; ambiguous cycle; continued fractions; reduced ideals; ambiguous classes of ideals; real quadratic fields; real quadratic order; ambiguous cycles of ideals},
language = {eng},
number = {2},
pages = {447-460},
publisher = {Université Bordeaux I},
title = {The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders},
url = {http://eudml.org/doc/247666},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Mollin, Richard A.
TI - The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 2
SP - 447
EP - 460
AB - Herein we introduce the palindromic index as a device for studying ambiguous cycles of reduced ideals with no ambiguous ideal in the cycle.
LA - eng
KW - quadratic order; class number; palindromic index; ambiguous cycle; continued fractions; reduced ideals; ambiguous classes of ideals; real quadratic fields; real quadratic order; ambiguous cycles of ideals
UR - http://eudml.org/doc/247666
ER -

References

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  1. [1] H. Cohn, A second course in number theory, John Wiley and Sons Inc., New York/London (1962). Zbl0208.31501MR133281
  2. [2] H. Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin, Graduate Texts in Mathematics138, (1993). Zbl0786.11071MR1228206
  3. [3] F. Halter-Koch, Prime-producing quadratic polynomials and class numbers of quadratic orders in Computational Number Theory, (A. Pethô, M. Pohst, H.C. Williams, and H.G. Zimmer eds.) Walter de Gruyter, Berlin (1991), 73—82. Zbl0728.11049MR1151856
  4. [4] F. Halter-Koch, P. Kaplan, K.S. Williams and Y. Yamamoto, Infrastructure des Classes Ambiges D'Idéaux des ordres des corps quadratiques réels, L'Enseignement Math37 (1991), 263—292. Zbl0756.11030MR1151751
  5. [5] P. Kaplan and K.S. Williams, The distance between ideals in the orders of real quadratic fields, L'Enseignment Math.36 (1990), 321-358. Zbl0726.11024MR1096423
  6. [6] S. Louboutin, Groupes des classes d'ideaux triviaux, Acta. Arith.LIV (1989), 61-74. Zbl0634.12008MR1024418
  7. [7] S. Louboutin, R.A. Mollin and H.C. Williams, Class numbers of real quadratic fields, continued fractions, raeduced ideals, prime-producing quadratic polynomials, and quadratic residue covers, Can. J. Math.44 (1992), 824-842. Zbl0771.11039MR1178571
  8. [8] R.A. Mollin, Ambiguous Classes in Real Quadratic Fields, Math Comp.61 (1993), 355-360. Zbl0790.11076MR1195434
  9. [9] R.A. Mollin and H.C. Williams, Classification and enumeration of real quadratic fields having exactly one non-inert prime less than a Minkowski bound, Can. Math. Bull.36 (1993), 108-115. Zbl0803.11054MR1205902
  10. [10] H.C. Williams and M.C. Wunderlich, On the parallel generation of the residues for the continued fraction factoring algorithm, Math. Comp.77 (1987), 405-423. Zbl0617.10005MR866124

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