Nagoya Mathematical Journal

On the class number and unit index of simplest quartic fields

Andrew J. Lazarus

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 121 (1991), 1-13.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118782779

Mathematical Reviews number (MathSciNet)
MR1096465

Zentralblatt MATH identifier
0719.11073

Subjects
Primary: 11R29: Class numbers, class groups, discriminants
Secondary: 11R16: Cubic and quartic extensions

Citation

Lazarus, Andrew J. On the class number and unit index of simplest quartic fields. Nagoya Math. J. 121 (1991), 1--13. https://projecteuclid.org/euclid.nmj/1118782779


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References

  • [1] Morris Abramowitz and Irene A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1964.
  • [2] Lyliane Bouvier and Jean-Jacques Payan, Modules sur certains anneaux de Dede- kind, J. Heine Angew. Math., 274/275 (1975), 278-286.
  • [3] Gary Cornell and Lawrence C. Washington, Class number of cyclotomic fields, J. Number Theory, 21(3) (1985), 260-274.
  • [4] Dennis A. Garbanati, Units with norm –1 and signatures of units, J. Reine Angew. Math., 283/284 (1976), 164-175.
  • [5] Marie-Nicole Gras, Table Numerique du Nombre de Classes et des Unites des Ex- tensions Cycliques de Degre 4 de Q, Publ. math. fasc. 2, Fac. Sci. Besanon, 1977/ 1978.
  • [6] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Cla- rendon Press, Oxford, Fourth edition, 1975.
  • [7] Helmut Hasse, Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkrpern, In Mathematische Abhand- lungen, pages 285-379, Walter de Gruyter, Berlin, 1975, Originally published 1950.
  • [8] Helmut Hasse, ber die Klassenzahl abelscher Zahlkrper, Akademie-Verlag, Berlin, 1952.
  • [9] Loo Keng Hua, Introduction to Number Theory, Springer-Verlag, Berlin, Heidel- berg, New York, revised English edition, 1982.
  • [10] Andrew J. Lazarus, The Class Number and Cyclotomy of Simplest Quartic Fields, PhD thesis, University of California, Berkeley, 1989.
  • [11] Class numbers of simplest quartic fields, In R. A. Mollin, editor, Number Theory, pages 313-323, Walter de Gruyter, Berlin, New York, 1990.
  • [12] Class numbers of simplest quartic fields, Gaussian periods and units in certain cyclic fields, to appear in Proc. Amer. Math. Soc.
  • [13] H. W. Leopoldt, ber Einheitengruppe und Klassenzahl reeller abelscher Zahl- krper, Abh. Deutsche Akad. Wiss. Berlin, 2 (1953), 1-48.
  • [14] R. A. Mollin and Hugh C. Williams, On prime-valued polynomials and class num- bers of real quadratic fields, Nagoya Math. J., 112 (1988), 143-151.
  • [15] Rene Schoof and Lawrence C. Washington, Quintic polynomials and real cyclotomic
  • [16] Daniel Shanks, The simplest cubic fields, Math. Comp.,2 (128) (1974), 1137-1152.
  • [17] H. M. Stark, Some effective cases of the Brauer-Siegel theorem, Invent, math., 23 (1974),135-152. Department of Mathematics and Computer Science University of California,Riverside Riverside, CA 92521 U.S.A.