Skip to main content
Log in

Integral bases and fundamental units of the cubic fieldsQ(w) defined by W3 + AW - 1 = 0defined by W3 + AW - 1 = 0

  • Published:
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. A.A. Albert. A Determination of the Integers of all Cubic Fields. Ann. of Math.31 (1930), 550–566.

    Article  MathSciNet  Google Scholar 

  2. L. Bernstein. Zeros of the Function\(f(n) = \sum {( - 1)^i (_i^{n - 2i} )} \). J. Number Theory6 (1974), 264–270.

    Article  MATH  MathSciNet  Google Scholar 

  3. W.E. Berwick. Algebraic Number Fields with Two Independent Units. Proc. London Math. Soc.34 (1932), 360–378.

    Article  MATH  Google Scholar 

  4. B.N. Delone and D.K. Faddeev. The Theory of Irrationalities of the Third Degree. Trudy Mat. Inst. Steklov (1940), Trans. Amer. Math. Soc.10 (1955).

  5. D. Hilbert. Über den Dirichletschen biquadratischen Zahlkörper. Math. Ann.45 (1894), 309–340. Gesammelte Abhandlungen I, 5, 24-52.

    Article  MathSciNet  Google Scholar 

  6. T. Honda. Pure Cubic Fields whose Class Numbers are Multiples of Three. J. Number Theory3 (1971), 7–12.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Ishida. Fundamental Units of certain Algebraic Number Fields. Abh. Math. Sem. Univ. Hamburg39 (1973), 245–250.

    Article  MATH  MathSciNet  Google Scholar 

  8. K. Komatsu. Integral Bases in Algebraic Number Fields. J. Reine Angew. Math.278/279 (1975), 137–144.

    MathSciNet  Google Scholar 

  9. P. Llorente, E. Nart andN. Vila. Discriminants of Number Fields Defined by Trinomials. Acta Arith.43 (1984), 367–373.

    MATH  MathSciNet  Google Scholar 

  10. R. Morikawa. On Units of certain Cubic Number Fields. Abh. Math. Sem. Univ. Hamburg42 (1974), 72–77.

    MATH  MathSciNet  Google Scholar 

  11. H.N. Shapiro andG.H. Sparer. Minimal Bases for Cubic Fields. Comm. Pure Appl. Math.44 (1991), No. 8-9, 1121–1136.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Sommer. Vorlesungen über Zahlentheorie. Teubner, Leipzig 1907.

    MATH  Google Scholar 

  13. L. Tornheim. Minimal Bases and Inessential Discriminant Divisors for a Cubic Field. Pacific J. Math.5 (1955), 623–631.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takaku, A., Yoshimoto, S.I. Integral bases and fundamental units of the cubic fieldsQ(w) defined by W3 + AW - 1 = 0defined by W3 + AW - 1 = 0. Abh.Math.Semin.Univ.Hambg. 64, 235–247 (1994). https://doi.org/10.1007/BF02940787

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02940787

Keywords

Navigation