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.
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 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)
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 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)
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 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
