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, Tome 7 (1995) no. 2, pp. 447-460.

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

DOI : https://doi.org/10.5802/jtnb.151
Classification : 11R11,  11R29,  11R65
Mots clés: quadratic order, class number, palindromic index, ambiguous cycle, continued fractions, reduced ideals
@article{JTNB_1995__7_2_447_0,
     author = {Mollin, Richard A.},
     title = {The palindromic index - A measure of ambiguous cycles of reduced ideals without any ambiguous ideals in real quadratic orders},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {2},
     year = {1995},
     pages = {447-460},
     doi = {10.5802/jtnb.151},
     zbl = {0855.11054},
     mrnumber = {1378590},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_1995__7_2_447_0/}
}
Richard A. Mollin. 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, Tome 7 (1995) no. 2, pp. 447-460. doi : 10.5802/jtnb.151. https://jtnb.centre-mersenne.org/item/JTNB_1995__7_2_447_0/

[1] H. Cohn, A second course in number theory, John Wiley and Sons Inc., New York/London (1962). | MR 133281 | Zbl 0208.31501

[2] H. Cohen, A course in computational algebraic number theory, Springer-Verlag, Berlin, Graduate Texts in Mathematics 138, (1993). | MR 1228206 | Zbl 0786.11071

[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. | MR 1151856 | Zbl 0728.11049

[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 Math 37 (1991), 263-292. | MR 1151751 | Zbl 0756.11030

[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. | MR 1096423 | Zbl 0726.11024

[6] S. Louboutin, Groupes des classes d'ideaux triviaux, Acta. Arith. LIV (1989), 61-74. | MR 1024418 | Zbl 0634.12008

[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. | MR 1178571 | Zbl 0771.11039

[8] R.A. Mollin, Ambiguous Classes in Real Quadratic Fields, Math Comp. 61 (1993), 355-360. | MR 1195434 | Zbl 0790.11076

[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. | MR 1205902 | Zbl 0803.11054

[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. | MR 866124 | Zbl 0617.10005