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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 4 (1972), 537–556. MR 0313220, https://doi.org/10.1016/0022-314X(72)90027-3
  • [4] Maurice Craig, Irregular Discriminants, Dissertation, University of Michigan, Ann Arbor, Mich., 1972.
  • [5] 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
  • [6] E. S. Golod and I. R. Šafarevič, On the class field tower, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 261–272 (Russian). MR 0161852
  • [7] Peter Roquette, On class field towers, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 231–249. MR 0218331

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Additional Information

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