The class number one problem for the non-abelian normal CM-fields of degree 16

Stéphane Louboutin

Acta Arithmetica (1997)

  • Volume: 82, Issue: 2, page 173-196
  • ISSN: 0065-1036

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Stéphane Louboutin. "The class number one problem for the non-abelian normal CM-fields of degree 16." Acta Arithmetica 82.2 (1997): 173-196. <http://eudml.org/doc/207087>.

@article{StéphaneLouboutin1997,
author = {Stéphane Louboutin},
journal = {Acta Arithmetica},
keywords = {CM-field; relative class number; zeta function; dihedral octic CM-fields},
language = {eng},
number = {2},
pages = {173-196},
title = {The class number one problem for the non-abelian normal CM-fields of degree 16},
url = {http://eudml.org/doc/207087},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Stéphane Louboutin
TI - The class number one problem for the non-abelian normal CM-fields of degree 16
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 2
SP - 173
EP - 196
LA - eng
KW - CM-field; relative class number; zeta function; dihedral octic CM-fields
UR - http://eudml.org/doc/207087
ER -

References

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  1. [CH] P. E. Conner and J. Hurrelbrink, Class Number Parity, Ser. Pure Math. 8, World Sci., Singapore, 1988. 
  2. [Hof] J. Hoffstein, Some analytic bounds for zeta functions and class numbers, Invent. Math. 55 (1979), 37-47. Zbl0474.12009
  3. [Lef] Y. Lefeuvre, The class number one problem for dihedral CM-fields, in preparation. 
  4. [Lem] F. Lemmermeyer, Unramified quaternion extensions of quadratic number fields, to appear. Zbl0890.11031
  5. [LLO] F. Lemmermeyer, S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of degree 24, in preparation. Zbl1010.11063
  6. [Lou 1] S. Louboutin, Majorations explicites de ∣L(1,χ)∣, C. R. Acad. Sci. Paris 316 (1993), 11-14. Zbl0774.11051
  7. [Lou 2] S. Louboutin, On the class number one problem for non-normal quartic CM-fields, Tôhoku Math. J. 46 (1994), 1-12. 
  8. [Lou 3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434. Zbl0795.11058
  9. [Lou 4] S. Louboutin, Calcul du nombre de classes des corps de nombres, Pacific J. Math. 171 (1995), 455-467. 
  10. [Lou 5] S. Louboutin, Corps quadratiques à corps de classes de Hilbert principaux et à multiplication complexe, Acta Arith. 74 (1996), 121-140. 
  11. [Lou 6] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, J. London Math. Soc. 54 (1996), 227-238. Zbl0861.11064
  12. [Lou 7] S. Louboutin, Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres, J. Math. Soc. Japan, to appear. 
  13. [Lou 8] S. Louboutin, CM-fields with cyclic ideal class groups of 2-power orders, J. Number Theory, to appear. Zbl0881.11078
  14. [LouOka 1] 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
  15. [LouOka 2] S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of 2-power degrees, Proc. London Math. Soc., to appear. Zbl0891.11054
  16. [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
  17. [Odl] A. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math. 29 (1975), 275-286. Zbl0299.12010
  18. [Uch] K. Uchida, Imaginary abelian number fields with class number one, Tôhoku Math. J. 24 (1972), 487-499. Zbl0248.12007
  19. [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982. 
  20. [Yam] K. Yamamura, The determination of the imaginary abelian number fields with class-number one, Math. Comp. 62 (1994), 899-921. Zbl0798.11046
  21. [YPJK] H. S. Yang, Y. H. Park, S. W. Jung and S. H. Kwon, Determination of all octic dihedral CM-fields with class number two, preprint, 1996. 

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