Parity of class numbers and Witt equivalence of quartic fields

Jakubec, Stanislav; Marko, František; Szymiczek, Kazimierz

doi:10.1090/S0025-5718-1995-1308455-1

Parity of class numbers and Witt equivalence of quartic fields

Authors: Stanislav Jakubec, František Marko and Kazimierz Szymiczek
Journal: Math. Comp. 64 (1995), 1711-1715
MSC: Primary 11R29; Secondary 11E81, 11R16
DOI: https://doi.org/10.1090/S0025-5718-1995-1308455-1
Corrigendum: Math. Comp. 66 (1997), 927.
MathSciNet review: 1308455
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that 27 out of the 29 Witt equivalence classes of quartic number fields can be represented by fields of class number 1. It is known that the remaining two classes contain solely fields of even class numbers. We show that these two classes can be represented by fields of class number 2.

[1] Z. I. Borevič and I.R. Šafarevič, Number theory, 3rd rev. ed., "Nauka", Moscow, 1985. (Russian)
[2] Johannes Buchmann, David Ford, and Michael Pohst, Enumeration of quartic fields of small discriminant, Math. Comp. 61 (1993), no. 204, 873–879. MR 1176706, https://doi.org/10.1090/S0025-5718-1993-1176706-0
[3] A. Czogała, Personal communication.
[4] Stanislav Jakubec and František Marko, Witt equivalence classes of quartic number fields, Math. Comp. 58 (1992), no. 197, 355–368. MR 1094952, https://doi.org/10.1090/S0025-5718-1992-1094952-0
[5] R. Perlis, K. Szymiczek, P. E. Conner, and R. Litherland, Matching Witts with global fields, Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991) Contemp. Math., vol. 155, Amer. Math. Soc., Providence, RI, 1994, pp. 365–387. MR 1260721, https://doi.org/10.1090/conm/155/01393
[6] Kazimierz Szymiczek, Witt equivalence of global fields, Comm. Algebra 19 (1991), no. 4, 1125–1149. MR 1102331, https://doi.org/10.1080/00927879108824194
[7] Kazimierz Szymiczek, Witt equivalence of global fields. II. Relative quadratic extensions, Trans. Amer. Math. Soc. 343 (1994), no. 1, 277–303. MR 1176087, https://doi.org/10.1090/S0002-9947-1994-1176087-X