The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent ≤ 2

Stéphane Louboutin; Hee-Sun Yang; Soun-Hi Kwon

Mathematica Slovaca (2004)

  • Volume: 54, Issue: 5, page 535-574
  • ISSN: 0139-9918

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Louboutin, Stéphane, Yang, Hee-Sun, and Kwon, Soun-Hi. "The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$." Mathematica Slovaca 54.5 (2004): 535-574. <http://eudml.org/doc/32410>.

@article{Louboutin2004,
author = {Louboutin, Stéphane, Yang, Hee-Sun, Kwon, Soun-Hi},
journal = {Mathematica Slovaca},
keywords = {CM-field; class group; quartic field; octic field},
language = {eng},
number = {5},
pages = {535-574},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$},
url = {http://eudml.org/doc/32410},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Louboutin, Stéphane
AU - Yang, Hee-Sun
AU - Kwon, Soun-Hi
TI - The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$
JO - Mathematica Slovaca
PY - 2004
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 54
IS - 5
SP - 535
EP - 574
LA - eng
KW - CM-field; class group; quartic field; octic field
UR - http://eudml.org/doc/32410
ER -

References

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  2. LANG S., Cyclotomic Fields I and II, (combined 2nd ed.). Grad. Texts in Math. 121, Springer-Verlag, New York, 1990. (1990) Zbl0704.11038MR1029028
  3. LANG S., Algebraic Number Theory, (2nd ed.). Grad. Texts in Math. 110, Springer-Verlag, New York, 1994. (1994) Zbl0811.11001MR1282723
  4. LOUBOUTIN S.-OKAZAKI R., Determination of all non-normal quartic C M -fields and of all non-abelian normal octic C M -fields with class number one, Acta Arith. 67 (1994), 47-62. (1994) Zbl0809.11069MR1292520
  5. LOUBOUTIN S.-OKAZAKI R., The class number one problem for some nonabelian normal C M -fields of 2-power degrees, Proc. London Math. Soc. (3) 76 (1998), 523-548. (1998) MR1616805
  6. LOUBOUTIN S.-OKAZAKI R., Determination of all quaternion C M -fields with ideal class groups of exponent 2, Osaka J. Math. 36 (1999), 229-257. (1999) Zbl0952.11025MR1736479
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  9. LOUBOUTIN S., Calcul du nombre de classes des corps de nombres, Pacific J. Math. 171 (1995), 455-467. (1995) Zbl0854.11060MR1372239
  10. LOUBOUTIN S., Determination of all nonquadratic imaginary cyclic number fields of 2-power degrees with ideal class groups of exponents < 2 , , Math. Comp. 64 (1995), 323-340. (1995) MR1248972
  11. LOUBOUTIN S., The class number one problem for the non-abelian normal C M -fields of degre 16, Acta Arith. 82 (1997), 173-196. (1997) MR1477509
  12. LOUBOUTIN S., Powerful necessary conditions for class number problems, Math. Nachr. 183 (1997), 173-184. (1997) Zbl0871.11078MR1434981
  13. LOUBOUTIN S., Hasse unit indices of dihedral octic C M -fields, Math. Nachr. 215 (2000), 107-113. Zbl0972.11105MR1768197
  14. LOUBOUTIN S., Explicit lower bounds for residues at s = 1 of Dedekind zeta functions and relative class numbers of C M -fields, Trans. Amer. Math. Soc. 355 (2003), 3079-3098. Zbl1026.11085MR1974676
  15. MORTON P., On Rédei's theory of the Pell equation, J. Reine Angew. Math. 307/308 (1979), 373-398. (1979) Zbl0395.12018MR0534233
  16. YANG H.-S.-KWON S.-H., The non-normal quartic C M -fields and the octic dihedral C M -fields with relative class number two, J. Number Theory 79 (1999), 175-193. (1999) Zbl0976.11051MR1728146

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