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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
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Abstract: A table of class numbers of real quadratic number fields with square-free determinant d, 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 are made, which are consistent with Gauss's related conjecture.
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Carl
Friedrich Gauss, Disquisitiones arithmeticae, Translated into
English by Arthur A. Clarke, S. J, Yale University Press, New Haven, Conn.,
1966. MR
0197380 (33 #5545)
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M.
D. Hendy, Applications of a continued fraction
algorithm to some class number problems, Math.
Comp. 28 (1974),
267–277. MR 0330102
(48 #8440), http://dx.doi.org/10.1090/S0025-5718-1974-0330102-2
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E. L. INCE, Cycles of Reduced Ideals in Quadratic Fields, Mathematical Tables, vol. IV, British Association for the Advancement of Science, London, 1934.
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K.
E. Kloss, Some number-theoretic calculations, J. Res. Nat.
Bur. Standards Sect. B 69B (1965), 335–336. MR 0190057
(32 #7473)
- [5]
K. E. KLOSS, M. NEWMAN & E. ORDMAN, Class Number of Primes of the Form
, National Bureau of Standards, 1965. (Deposited in the UMT file.)
- [6]
Richard
B. Lakein, Computation of the ideal class group
of certain complex quartic fields, Math.
Comp. 28 (1974),
839–846. MR 0374090
(51 #10290), http://dx.doi.org/10.1090/S0025-5718-1974-0374090-1
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D. SHANKS, Review of UMT file [5], Math. Comp., v. 23, 1969, pp. 213-214.
- [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
, 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.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1975-0409402-4
PII:
S 0025-5718(1975)0409402-4
Keywords:
Ideal classes,
continued-fraction expansion,
Lagrange algorithm,
ideal genera,
Dirichlet series,
fundamental unit
Article copyright:
© Copyright 1975 American Mathematical Society
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