Class number problems for dicyclic CM-fields

Publicationes Mathematicae Debrecen

Volumn 57, Issue 3-4, 2000, Pages 283-295

  Louboutin, Stéphane ^a   Park, Young Ho ^b  

^a UNIVERSITÉ DE CAEN   (France)

^b Korea University   (South Korea)

Author keywords

CM field; Dicyclic group; Zeta function

Indexed keywords

EID: 0034360430     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. A. FRöHLICH and J. QUEYRUT, On the functional equation of the Artin L-function for characters of real representations, Inventiones Math. 20 (1973), 125-138.
2. H. HIDA, Elementary theory of L-functions and Eisenstein series, London Mathematical Society, Student Texts, 26, Cambridge University Press, 1993.
3. Y. LEFEUVRE, Corps diédraux à multiplication complexe principaux, Ann. Inst. Fourier (Grenoble) (to appear).
4. S. LOUBOUTIN, R. OKAZAKI and M. OLIVIER, The class number one problem for some non-abelian normal CM-fields, Trans. Amer. Math. Soc. 349 (1997), 3657-3678.
5. S. LOUBOUTIN, CM-fields with cyclic ideal class groups of 2-power orders, J. of Number Theory 67 (1997), 1-10.
6. S. LOUBOUTIN, Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres, J. Math. Soc. Japan 50 (1998), 57-69.
7. S. LOUBOUTIN, Upper bounds on |L(1,χ)| and applications, Canad. J. Math. 50 (1998), 784-815.
8. S. LOUBOUTIN, Computation of relative class numbers of CM-fields by using Hecke L-functions, Math. Comp. 69 (2000), 371-393.
9. S. LOUBOUTIN, The class number one problem for the dihedral and dicyclic CM-fields, Colloq. Math. 80 (1999), 259-265.
10. S. LOUBOUTIN, Formulae for some Artin root numbers, Tatra Mountains Mathematical Publications (to appear).
11. 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.
12. S. LOUBOUTIN, Y.-H. PARK and Y. LEFEUVRE, Construction of the real dihedral number fields of degree 2p, Applications, Acta Arith. 89 (1999), 201-215.
13. J. MARTINET, Sur l'arithmétique des extensions à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier (Grenoble) 19 (1969), 1-80.
14. Y.-H. PARK and S.-H. KWON, Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20, Acta Arith. 83 (1998), 211-223.
15. L. C. WASHINGTON, Introduction to Cyclotomic Fields, Grad. Texts Math., 83, Springer-Verlag, 1982, 2nd edn: 1997.