On rappelle que O K = Z [µ m ] et que les nombres premiers ramifiés dans l'extension K/Q sont exactement les diviseurs de m. Soit p un nombre premier divisant m. Notons r = v p (m), e = (p ? 1) p r?1 , ? une racine primitive p r ième de l'unité ,
Capitulation dans certaines extensions non ramifiées de corps quartiques cycliques, Arch. Mat, vol.44, pp.271-284, 2008. ,
DOI : 10.4064/aa127-3-3
P -orderings and polynomial functions on arbitrary subsets of Dedekind rings, J. Reine Angew. Math, vol.490, pp.101-127, 1997. ,
Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain, Journal of Number Theory, vol.72, issue.1, pp.67-75, 1998. ,
DOI : 10.1006/jnth.1998.2220
Big projective modules are free, Illinois J. Math, vol.7, pp.24-31, 1963. ,
The 2-class group of certain biquadratic number fields I, J. reine angew, Math, pp.295-61, 1977. ,
The 2-class group of biquadratic fields. II, Pacific Journal of Mathematics, vol.78, issue.1, pp.11-26, 1978. ,
DOI : 10.2140/pjm.1978.78.11
Class Number and Ramification in Number Fields, Nagoya Mathematical Journal, vol.9, pp.97-101, 1963. ,
DOI : 10.1017/S002776300001120X
Integer-valued polynomials, Mathematical Surveys and Monographs Amer. Math. Soc, vol.48, 1997. ,
DOI : 10.1090/surv/048
Factorial Groups and Pólya groups in Galoisian Extension of Q, Lecture Notes in Pure and Applied Mathematics, vol.231, pp.77-86, 2003. ,
A Course in Computational Algebraic Number Theory, 2000. ,
DOI : 10.1007/978-3-662-02945-9
The genus field and genus group in finite number fields, Mathematika, vol.4, issue.01, pp.40-46, 1959. ,
DOI : 10.1112/S0025579300001911
Principal ideal theorems in the genus field for absolutely abelian extensions, Journal of Number Theory, vol.9, issue.1, pp.4-15, 1977. ,
DOI : 10.1016/0022-314X(77)90045-2
Units with norm ?1 and signatures of units, J. Reine Angew. Math, vol.283284, pp.164-175, 1976. ,
Multiplicative Ideal Theory, 1972. ,
Bases of integer-valued polynomials, Commutative ring theory 149, pp.97-116, 1991. ,
Polynômes à valeurs entières sur l'anneau des entiers de Gauss, C.R. Acad. Sc. Paris, Sér A, vol.307, pp.375-378, 1988. ,
On class field towers, Izv. Akad. Nauk, vol.28, pp.261-272, 1964. ,
DOI : 10.1090/trans2/048/05
Class Field Theory, 2005. ,
DOI : 10.1007/978-3-662-11323-3
URL : https://hal.archives-ouvertes.fr/hal-00259968
Calculation of the class numbers of imaginary cyclic quartic fields, Mathematics of Computation, vol.49, issue.180, p.pp, 1986. ,
DOI : 10.1090/S0025-5718-1987-0906194-5
Zur Geschlechtertheorie in quadratischen Zahlk??rpern, Journal of the Mathematical Society of Japan, vol.3, issue.1, pp.45-51, 1951. ,
DOI : 10.2969/jmsj/00310045
Die Theorie der algebraischen Zahlkörper, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol.4, pp.1894-95 ,
The integers of a cyclic quartic field, Rocky Mountain Journal of Mathematics, vol.20, issue.1, pp.145-150, 1990. ,
DOI : 10.1216/rmjm/1181073167
The Genus Fields of Algebraic Number Fields, 1976. ,
DOI : 10.1007/BFb0100829
On the genus field of an algebraic number field of odd prime degree, Journal of the Mathematical Society of Japan, vol.27, issue.2, pp.165-173, 1974. ,
DOI : 10.2969/jmsj/02720289
Zur Geschlechtertheorie in abelschen Zahlkörpern, Math. Nachr, vol.9, pp.350-362, 1953. ,
DOI : 10.1002/mana.19530090604
Über ganzwertige Polynome in algebraischen Zahlkörpren, J. reine angew. Math, vol.149, pp.117-124, 1919. ,
Über ganzwertige Polynome in algebraischen Zahlkörpern, J. Reine Angew. Math, vol.149, pp.97-116, 1919. ,
Classical Theory of Algebraic Numbers, 2000. ,
DOI : 10.1007/978-0-387-21690-4
On class field towers, Cassels and Fröhlich, Algebraic number theory (Proc. Instructional Conf, pp.231-249, 1965. ,
The conductor of a cyclic quartic field using Gauss sums, Czechoslovak Mathematical Journal, vol.47, issue.3, pp.47-453, 1997. ,
DOI : 10.1023/A:1022407300351
Algebraic function fields and codes, 1993. ,
Sur la capitulation dans les corps de genres d'une extension ab??lienne d'un corps quadratique imaginaire, Journal of Number Theory, vol.85, issue.1, pp.92-107, 2000. ,
DOI : 10.1006/jnth.2000.2550
Integers of biquadratic fields, Bulletin canadien de math??matiques, vol.13, issue.0, pp.519-526, 1970. ,
DOI : 10.4153/CMB-1970-094-8
Integer valued polynomials over a number field, Manuscripta Mathematica, vol.27, issue.2-3, pp.155-203, 1982. ,
DOI : 10.1007/BF01174875