On some families of imaginary quadratic fields

Author:
F. Diaz y Diaz

Journal:
Math. Comp. **32** (1978), 637-650

MSC:
Primary 12A25

DOI:
https://doi.org/10.1090/S0025-5718-1978-0485775-4

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]**D. A. BUELL, "Class groups of quadratic fields,"*Math. Comp.*, v. 30, 1976, pp. 610-623. MR**0404205 (53:8008)****[2]**M. CRAIG, "A type of class group for imaginary quadratic fields,"*Acta Arith.*, v. 22, 1973, pp. 449-459. MR**0318098 (47:6647)****[3]**F. DIAZ Y DIAZ, "Sur les corps quadratiques imaginaires dont le 3-rang du groupe des classes est supérieur à 1,"*Séminaire Delange-Pisot-Poitou*, 1973/74, G-15.**[4]**S. KURODA, "On the class number of imaginary quadratic number fields,"*Proc. Japan Acad.*, v. 40, 1964, pp. 365-367. MR**0170882 (30:1117)****[5]**C. NEILD & D. SHANKS, "On the 3-rank of quadratic fields and the Euler product,"*Math. Comp.*, v. 28, 1974, pp. 279-291. 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. 415-440. 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. 71-87. 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. 537-556. MR**0313220 (47:1775)****[9]**D. SHANKS & R. SERAFIN, "Quadratic fields with four invariants divisible by 3,"*Math. Comp.*, v. 27, 1973, pp. 183-187. 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. 173-178. MR**0399039 (53:2890)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0485775-4

Article copyright:
© Copyright 1978
American Mathematical Society