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Quadratic fields with four invariants divisible by $ 3$


Authors: Daniel Shanks and Richard Serafin
Journal: Math. Comp. 27 (1973), 183-187
MSC: Primary 12A25; Secondary 12A50
DOI: https://doi.org/10.1090/S0025-5718-1973-0330097-0
Corrigendum: Math. Comp. 27 (1973), 1012.
Corrigendum: Math. Comp. 27 (1973), 1011-1012.
MathSciNet review: 0330097
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Abstract: Imaginary quadratic fields are developed that have four invariants divisible by 3. Their associated real fields are found to differ in one significant respect: one case has two elementary generators and the other has only one.


References [Enhancements On Off] (What's this?)

  • [1] A. Scholz, "Über die Beziehung der Klassenzahlen quadratischer Körper zueinander," Crelle's J., v. 166, 1932, pp. 201-203.
  • [2] A. Scholz & Olga Taussky, "Die Hauptideale der kubischen Klassenkörper imaginär quadratischer Zahlkörper: ihre rechnerische Bestimmung und ihr Einfluss auf den Klassenkörperturm," Crelle's J., v. 171, 1934, pp. 19-41.
  • [3] Daniel Shanks, "New types of quadratic fields having three invariants divisible by 3," J. Number Theory. (To appear.) MR 0313220 (47:1775)
  • [4] Maurice Craig, Irregular Discriminants, Dissertation, University of Michigan, Ann Arbor, Mich., 1972.
  • [5] Daniel Shanks & Peter Weinberger, "A quadratic field of prime discriminant requiring three generators for its class group, and related theory," Sierpiński Memorial Volume, Acta Arith., 1972, pp. 71-87. MR 0309899 (46:9003)
  • [6] E. S. Golod & I. R. Šafarevič, "On class field towers," Izv. Akad. Nauk SSSR, v. 28, 1964, pp. 261-272. (Russian) MR 0161852 (28:5056)
  • [7] Peter Roquette, "On class field towers," in Algebraic Number Theory, Thompson, Washington, D.C., 1967. MR 0218331 (36:1418)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1973-0330097-0
Article copyright: © Copyright 1973 American Mathematical Society

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