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ArticleOriginal scientific text

Title

Determination of all imaginary abelian sextic number fields with class number ≤ 11

Authors 1, 2

Affiliations

  1. Department of Mathematics, Korea University, 136-701 Seoul, Korea
  2. Department of Mathematics Education, Korea University, 136-701, Seoul, Korea

Bibliography

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  4. [M.N.G.] M.-N. Gras, Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de ℚ, J. Reine Angew. Math. 277 (1975), 89-116.
  5. [L1] S. Louboutin, Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux, Acta Arith. 62 (1992), 109-124.
  6. [L2] S. Louboutin, Majorations explicites de |L(1,χ)|, C. R. Acad. Sci. Paris 316 (1993), 11-14.
  7. [L3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434.
  8. [LO] S. Louboutin and R. Okazaki, Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one, Acta Arith. 67 (1994), 47-62.
  9. [LOO] S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, Trans. Amer. Math. Soc., to appear.
  10. [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140.
  11. [MW] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542.
  12. [S1] H. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.
  13. [S2] H. Stark, On complex quadratic fields with class-number two, Math. Comp. 29 (1975), 289-302.
  14. [Wg] C. Wagner, Class number 5, 6 and 7, Math. Comp. 65 (1996), 785-800.
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  16. [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921.
Acta Arithmetica
1997/82/1
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Pages:
27-43
Main language of publication
English
Received
1996-05-25
Accepted
1997-02-18
Published
1997
Exact and natural sciences