On a problem of Eisenstein

Peter Stevenhagen

Acta Arithmetica (1996)

  • Volume: 74, Issue: 3, page 259-268
  • ISSN: 0065-1036

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Peter Stevenhagen. "On a problem of Eisenstein." Acta Arithmetica 74.3 (1996): 259-268. <http://eudml.org/doc/206851>.

@article{PeterStevenhagen1996,
author = {Peter Stevenhagen},
journal = {Acta Arithmetica},
keywords = {quadratic units; cubic fields; Eisenstein's fourth problem; 3-divisibility of the class number; cubic number fields},
language = {eng},
number = {3},
pages = {259-268},
title = {On a problem of Eisenstein},
url = {http://eudml.org/doc/206851},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Peter Stevenhagen
TI - On a problem of Eisenstein
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 3
SP - 259
EP - 268
LA - eng
KW - quadratic units; cubic fields; Eisenstein's fourth problem; 3-divisibility of the class number; cubic number fields
UR - http://eudml.org/doc/206851
ER -

References

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  1. [1] W. Bosma and P. Stevenhagen, Density computations for real quadratic units, Math. Comp., to appear. Zbl0859.11064
  2. [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. [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. Zbl0523.12002
  4. [4] D. A. Cox, Primes of the Form x²+ny², Wiley-Interscience, 1989. 
  5. [5] H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, I, Bull. London Math. Soc. 1 (1969), 345-348. Zbl0211.38602
  6. [6] H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, II, Proc. Roy. Soc. London A 322 (1971), 405-420. Zbl0212.08101
  7. [7] G. Eisenstein, Aufgaben, J. Reine Angew. Math. 27 (1844), 86-88; see also: Mathematische Werke, Band I, Chelsea, 111-113. 
  8. [8] H. Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischen Grundlage, Math. Z. 31 (1930), 565-582. Zbl56.0167.02
  9. [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. [10] P. Stevenhagen, The number of real quadratic fields having units of negative norm, Experiment. Math. 2 (1993), 121-136. Zbl0792.11041
  11. [11] P. Stevenhagen, A density conjecture for the negative Pell equation, in: Computational Algebra and Number Theory, Sydney 1992, Kluwer, 1995, 187-200. Zbl0838.11066
  12. [12] P. Stevenhagen, Divisibility by 2-powers of certain quadratic class numbers, J. Number Theory 43 (1993), 1-19. Zbl0767.11054
  13. [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. Zbl0393.12008

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