Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



The distribution of ideal class numbers of real quadratic fields

Author: M. D. Hendy
Journal: Math. Comp. 29 (1975), 1129-1134
MSC: Primary 12A25; Secondary 12A50
Corrigendum: Math. Comp. 30 (1976), 679.
Corrigendum: Math. Comp. 30 (1976), 679.
MathSciNet review: 0409402
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A table of class numbers of real quadratic number fields $ Q(\surd d)$ with square-free determinant d, $ 1000 < d < 100000$ is examined and several analyses of the distribution of the class numbers, and the number of classes per genus are made. From these, two conjectures on the possible distribution of the class numbers as $ d \to \infty $ are made, which are consistent with Gauss's related conjecture.

References [Enhancements On Off] (What's this?)

  • [1] C. F. GAUSS, Disquisitiones Arithmeticae, Fleischer, Leipzig, 1870; English transl., Yale Univ. Press, New Haven, Conn., 1966. MR 33 #5545. MR 0197380 (33:5545)
  • [2] M. D. HENDY, "Applications of a continued fraction algorithm to some class number problems," Math. Comp., v. 28, 1974, pp. 267-277. MR 48 #8440. MR 0330102 (48:8440)
  • [3] E. L. INCE, Cycles of Reduced Ideals in Quadratic Fields, Mathematical Tables, vol. IV, British Association for the Advancement of Science, London, 1934.
  • [4] K. E. KLOSS, "Some number-theoretic calculations," J. Res. Nat. Bur. Standards Sect. B, v. 69B, 1965, pp. 335-336. MR 32 #7473. MR 0190057 (32:7473)
  • [5] K. E. KLOSS, M. NEWMAN & E. ORDMAN, Class Number of Primes of the Form $ 4n + 1$, National Bureau of Standards, 1965. (Deposited in the UMT file.)
  • [6] R. B. LAKEIN, "Computation of the ideal class group of certain complex quartic fields," Math. Comp., v. 28, 1974, pp. 839-846. MR 0374090 (51:10290)
  • [7] D. SHANKS, Review of UMT file [5], Math. Comp., v. 23, 1969, pp. 213-214.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A25, 12A50

Retrieve articles in all journals with MSC: 12A25, 12A50

Additional Information

Keywords: Ideal classes, continued-fraction expansion, Lagrange algorithm, ideal genera, Dirichlet series, fundamental unit
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society