A note on class-number one in certain real quadratic and pure cubic fields

Mathematics of Computation

Volumn 46, Issue 173, 1986, Pages 333-336

  Tennenhouse, M ^a   Williams, H C ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966219484     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1986-0815853-3     Document Type: Article

References (13)

1. H. Cohen, “Sur la distribution asymptotique des groupes de classes, ” C. R. Acad. Sci. Paris Ser. J Math., v. 296, 1983, pp. 245-246.
2. H. Eisenbeis, G. Frey & B. Ommerborn, “Computation of the 2-rank of pure cubic fields, ” Math. Comp., v. 32, 1978, pp. 559-569.
3. T. Honda, “Pure cubic fields whose class numbers are multiples of three, ” J. Number Theory, v. 3, 1971, pp. 7-12.
4. S. Kuroda, “Table of class numbers h(p)> 1 for quadratic fields Q(Jp), p < 2776817, ” Math. Comp., v. 29, 1975, pp. 335-336, UMT File.
5. R. B. Lakein, “Computation of the ideal class group of certain complex quartic fields, II, ” Math. Comp., v. 29, 1975, pp. 137-144.
6. H. W. Lenstra, On the Calculation of Regulators and Class Numbers of Quadratic Fields, London Math. Soc. Lecture Note Series, no. 56, 1982, pp. 123-150.
7. R. SCHOOF, “Quadratic fields and factorization, ” Computational Methods in Number Theory, Part II, Math. Centrum Tracts, No. 155, Amsterdam, 1983, pp. 235-286.
8. D. Shanks, Class Number, A Theory of Factorization, and Genera, Proc. Sympos. Pure Math., Vol. 20 (1969 Institute on Number Theory), Amer. Math. Soc., Providence, R. I., 1971, pp. 415-440.
9. H. C. Williams, “Improving the speed of calculating the regulator of certain pure cubic fields, ” Math. Comp., v. 35, 1980, pp. 1423-1434.
10. H. C. Williams, “Continued fractions and number-theoretic computations” (Proc. Number Theory Conf. Edmonton 1983), Rocky Mountain J. Math., v. 15, 1985, pp. 621-655.
11. H. C. Williams & J. Broere, “A computational technique for evaluating L(l, x) and the class number of a real quadratic field, ” Math. Comp., v. 30, 1976, pp. 887-893.
12. H. C. Williams, G. W. Dueck & B. K. Schmid, “A rapid method of evaluating the regulator and class number of a pure cubic field, ” Math. Comp., v. 41, 1983, pp. 235-286.
13. H. C. Williams & D. Shanks, “A note on class-number one in pure cubic fields, ” Math. Comp., v. 33, 1979, pp. 1317-1320.