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]**Duncan A. Buell,*Class groups of quadratic fields*, Math. Comp.**30**(1976), no. 135, 610–623. MR**0404205**, https://doi.org/10.1090/S0025-5718-1976-0404205-X**[2]**Maurice Craig,*A type of class group for imaginary quadratic fields*, Acta Arith.**22**(1973), 449–459. (errata insert). MR**0318098****[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]**Sige-Nobu Kuroda,*On the class number of imaginary quadratic number fields*, Proc. Japan Acad.**40**(1964), 365–367. MR**0170882****[5]**Carol Neild and Daniel Shanks,*On the 3-rank of quadratic fields and the Euler product*, Math. Comp.**28**(1974), 279–291. MR**0352042**, https://doi.org/10.1090/S0025-5718-1974-0352042-5**[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****[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****[8]**Daniel Shanks,*New types of quadratic fields having three invariants divisible by 3*, J. Number Theory**4**(1972), 537–556. MR**0313220**, https://doi.org/10.1016/0022-314X(72)90027-3**[9]**Daniel Shanks and Richard Serafin,*Quadratic fields with four invariants divisible by 3*, Math. Comp.**27**(1973), 183–187. MR**0330097**, https://doi.org/10.1090/S0025-5718-1973-0330097-0

Daniel Shanks,*Corrigenda: “Quadratic fields with four invariants divisible by 3” (Math. Comp. 27 (1973), 183–187) by Daniel Shanks and Richard Serafin*, Math. Comp.**27**(1973), 1012. MR**0330098**, https://doi.org/10.1090/S0025-5718-1973-0330098-2**[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**, https://doi.org/10.1090/S0025-5718-1976-0399039-9

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Additional Information

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

Article copyright:
© Copyright 1978
American Mathematical Society