On some families of imaginary quadratic fields
Author:
F. Diaz y Diaz
Journal:
Math. Comp. 32 (1978), 637650
MSC:
Primary 12A25
MathSciNet review:
0485775
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Abstract: This paper gives a method of obtaining imaginary quadratic fields whose class groups have at least three invariants divisible by 3. Complementary calculations have yielded a large number of imaginary quadratic fields having class groups with four invariants divisible by 3. Some numerical examples, previously unknown, are included.
 [1]
Duncan
A. Buell, Class groups of quadratic
fields, Math. Comp. 30
(1976), no. 135, 610–623. MR 0404205
(53 #8008), http://dx.doi.org/10.1090/S0025571819760404205X
 [2]
Maurice
Craig, A type of class group for imaginary quadratic fields,
Acta Arith. 22 (1973), 449–459. (errata insert). MR 0318098
(47 #6647)
 [3]
F. DIAZ Y DIAZ, "Sur les corps quadratiques imaginaires dont le 3rang du groupe des classes est supérieur à 1," Séminaire DelangePisotPoitou, 1973/74, G15.
 [4]
SigeNobu
Kuroda, On the class number of imaginary quadratic number
fields, Proc. Japan Acad. 40 (1964), 365–367.
MR
0170882 (30 #1117)
 [5]
Carol
Neild and Daniel
Shanks, On the 3rank of quadratic fields and
the Euler product, Math. Comp. 28 (1974), 279–291. MR 0352042
(50 #4530), http://dx.doi.org/10.1090/S00255718197403520425
 [6]
Daniel
Shanks, Class number, a theory of factorization, and genera,
1969 Number Theory Institute (Proc. Sympos. Pure Math., Vol. XX, State
Univ. New York, Stony Brook, N.Y., 1969), Amer. Math. Soc., Providence,
R.I., 1971, pp. 415–440. MR 0316385
(47 #4932)
 [7]
Daniel
Shanks and Peter
Weinberger, A quadratic field of prime discriminant requiring three
generators for its class group, and related theory, Acta Arith.
21 (1972), 71–87. MR 0309899
(46 #9003)
 [8]
Daniel
Shanks, New types of quadratic fields having three invariants
divisible by 3, J. Number Theory 4 (1972),
537–556. MR 0313220
(47 #1775)
 [9]
Daniel
Shanks and Richard
Serafin, Quadratic fields with four invariants
divisible by 3, Math. Comp. 27 (1973), 183–187. MR 0330097
(48 #8436a), http://dx.doi.org/10.1090/S00255718197303300970
 [10]
Daniel
Shanks, Class groups of the quadratic fields
found by F. Diaz y Diaz, Math. Comp.
30 (1976), no. 133, 173–178. MR 0399039
(53 #2890), http://dx.doi.org/10.1090/S00255718197603990399
 [1]
 D. A. BUELL, "Class groups of quadratic fields," Math. Comp., v. 30, 1976, pp. 610623. MR 0404205 (53:8008)
 [2]
 M. CRAIG, "A type of class group for imaginary quadratic fields," Acta Arith., v. 22, 1973, pp. 449459. MR 0318098 (47:6647)
 [3]
 F. DIAZ Y DIAZ, "Sur les corps quadratiques imaginaires dont le 3rang du groupe des classes est supérieur à 1," Séminaire DelangePisotPoitou, 1973/74, G15.
 [4]
 S. KURODA, "On the class number of imaginary quadratic number fields," Proc. Japan Acad., v. 40, 1964, pp. 365367. MR 0170882 (30:1117)
 [5]
 C. NEILD & D. SHANKS, "On the 3rank of quadratic fields and the Euler product," Math. Comp., v. 28, 1974, pp. 279291. MR 0352042 (50:4530)
 [6]
 D. SHANKS, "Class number, a theory of factorization and genera," Proc. Sympos. Pure Math., Vol. 20, Amer. Math. Soc., Providence, R. I., 1971, pp. 415440. MR 0316385 (47:4932)
 [7]
 D. SHANKS & P. WEINBERGER, "A quadratic field of prime discriminant requiring three generators for its class group, and related theory," Acta Arith., v. 21, 1972, pp. 7187. MR 0309899 (46:9003)
 [8]
 D. SHANKS, "New types of quadratic fields having three invariants divisible by 3," J. Number Theory, v. 4, 1972, pp. 537556. MR 0313220 (47:1775)
 [9]
 D. SHANKS & R. SERAFIN, "Quadratic fields with four invariants divisible by 3," Math. Comp., v. 27, 1973, pp. 183187. MR 0330097 (48:8436a)
 [10]
 D. SHANKS, "Class groups of the quadratic fields found by F. Diaz y Diaz," Math. Comp., v. 30, 1976, pp. 173178. MR 0399039 (53:2890)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804857754
PII:
S 00255718(1978)04857754
Article copyright:
© Copyright 1978 American Mathematical Society
