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ArticleOriginal scientific text

Title

On a problem of Eisenstein

Authors 1

Affiliations

  1. Faculteit Wiskunde en Informatica, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, the Netherlands

Keywords

ENG
quadratic units, cubic fields

Bibliography

  1. W. Bosma and P. Stevenhagen, Density computations for real quadratic units, Math. Comp., to appear.
  2. H. Cohen and H. W. Lenstra, Jr., Heuristics on class groups of number fields, in: Number Theory, Noordwijkerhout 1983, H. Jager (ed.), Lecture Notes in Math. 1068, Springer, 1984, 33-62.
  3. H. Cohn and J. C. Lagarias, On the existence of fields governing the 2-invariants of the class groups of ℚ(√dp) as p varies, Math. Comp. 41 (1983), 711-730.
  4. D. A. Cox, Primes of the Form x²+ny², Wiley-Interscience, 1989.
  5. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, I, Bull. London Math. Soc. 1 (1969), 345-348.
  6. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, II, Proc. Roy. Soc. London A 322 (1971), 405-420.
  7. G. Eisenstein, Aufgaben, J. Reine Angew. Math. 27 (1844), 86-88; see also: Mathematische Werke, Band I, Chelsea, 111-113.
  8. H. Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischen Grundlage, Math. Z. 31 (1930), 565-582.
  9. A. J. Stephens and H. C. Williams, Some computational results on a problem of Eisenstein, in: Théorie des Nombres - Number Theory, J. W. M. de Koninck and C. Levesque (eds.), de Gruyter, 1992, 869-886.
  10. P. Stevenhagen, The number of real quadratic fields having units of negative norm, Experiment. Math. 2 (1993), 121-136.
  11. P. Stevenhagen, A density conjecture for the negative Pell equation, in: Computational Algebra and Number Theory, Sydney 1992, Kluwer, 1995, 187-200.
  12. P. Stevenhagen, Divisibility by 2-powers of certain quadratic class numbers, J. Number Theory 43 (1993), 1-19.
  13. K. S. Williams, On the class number of ℚ(√-p) modulo 16, for p ≡ 1 mod 8 a prime, Acta Arith. 39 (1981), 381-398.
Acta Arithmetica
1996/74/3
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Pages:
259-268
Main language of publication
English
Received
1995-04-18
Accepted
1995-05-29
Published
1996
Exact and natural sciences