Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
Corrigendum: Math. Comp. 27 (1973), 1012.
Corrigendum: Math. Comp. 27 (1973), 1011-1012.
MathSciNet review: 0330097
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 313220,
  • [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 309899,
  • [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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 12A25, 12A50

Retrieve articles in all journals with MSC: 12A25, 12A50

Additional Information

Article copyright: © Copyright 1973 American Mathematical Society