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

Young-Ho Park; Soun-Hi Kwon

Acta Arithmetica (1997)

  • Volume: 82, Issue: 1, page 27-43
  • ISSN: 0065-1036

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Young-Ho Park, and Soun-Hi Kwon. "Determination of all imaginary abelian sextic number fields with class number ≤ 11." Acta Arithmetica 82.1 (1997): 27-43. <http://eudml.org/doc/207076>.

@article{Young1997,
author = {Young-Ho Park, Soun-Hi Kwon},
journal = {Acta Arithmetica},
keywords = {imaginary abelian sextic number fields; lower bounds for the relative class number; upper bounds for the conductors; abelian sextic CM-fields with small class number},
language = {eng},
number = {1},
pages = {27-43},
title = {Determination of all imaginary abelian sextic number fields with class number ≤ 11},
url = {http://eudml.org/doc/207076},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Young-Ho Park
AU - Soun-Hi Kwon
TI - Determination of all imaginary abelian sextic number fields with class number ≤ 11
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 1
SP - 27
EP - 43
LA - eng
KW - imaginary abelian sextic number fields; lower bounds for the relative class number; upper bounds for the conductors; abelian sextic CM-fields with small class number
UR - http://eudml.org/doc/207076
ER -

References

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  1. [A1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334. 
  2. [A2] S. Arno, M. L. Robinson and F. S. Wheeler, Imaginary quadratic fields with small odd class number, Algebraic Number Theory Archives, 1993, 1-34; Acta Arith., to appear. 
  3. [G.G] G. Gras, Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l, Ann. Inst. Fourier (Grenoble) 23 (3) (1973), 1-48; 23 (4) (1973), 1-44. Zbl0276.12013
  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. Zbl0774.11051
  7. [L3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434. Zbl0795.11058
  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. Zbl0809.11069
  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. Zbl0893.11045
  10. [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140. Zbl0207.05602
  11. [MW] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542. Zbl0285.12004
  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. Zbl0321.12009
  14. [Wg] C. Wagner, Class number 5, 6 and 7, Math. Comp. 65 (1996), 785-800. 
  15. [Ws] L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983. 
  16. [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921. Zbl0798.11046

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