@article{bwmeta1.element.bwnjournal-article-aav74i2p121bwm,
author = {St\'ephane Louboutin},
title = {Corps quadratiques \`a corps de classes de Hilbert principaux et \`a multiplication complexe},
journal = {Acta Arithmetica},
volume = {76},
year = {1996},
pages = {121-140},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav74i2p121bwm}
}
Stéphane Louboutin. Corps quadratiques à corps de classes de Hilbert principaux et à multiplication complexe. Acta Arithmetica, Tome 76 (1996) pp. 121-140. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav74i2p121bwm/
[000] [Coh] H. Cohen, A Course in Computational Algebraic Number Theory, Springer, 1994.
[001] [C-C] H. Cohn and G. Cooke, Parametric form of an eight class field, Acta Arith. 30 (1976), 367-377. | Zbl 0299.12004
[002] [Cox] D. A. Cox, Primes of the Form x²+ny², Wiley, 1989. | Zbl 1275.11002
[003] [D-P] P. Damey et J. J. Payan, Existence et construction des extensions galoisiennes et non abéliennes de degré 8 d'un corps de caractéristique différente de 2, J. Reine Angew. Math. 244 (1970), 37-54. | Zbl 0206.34401
[004] [Hal] M. Hall, The Theory of Groups, Chapter 12, Macmillan, New York, 1959.
[005] [Hof] J. Hoffstein, Some analytic bounds for zeta functions and class numbers, Invent. Math. 55 (1979), 37-47. | Zbl 0474.12009
[006] [Lou 1] S. Louboutin, Norme relative de l'unité fondamentale et 2-rang du groupe des classes d'idéaux de certains corps biquadratiques, Acta Arith. 58 (1991), 273-288. | Zbl 0703.11050
[007] [Lou 2] S. Louboutin, Calcul des nombres de classes relatifs de certains corps de classes de Hilbert, C. R. Acad. Sci. Paris 319 (1994), 321-325.
[008] [Lou 3] S. Louboutin, Determination of all quaternion octic CM-fields with class number two, J. London Math. Soc., to appear.
[009] [Lou-Oka] 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. | Zbl 0809.11069
[010] [M-M] J. M. Masley and H. L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256. | Zbl 0335.12013
[011] [M-W] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542. | Zbl 0285.12004
[012] [Odl 1] A. M. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math. 29 (1975), 275-286. | Zbl 0299.12010
[013] [Odl 2] A. M. Odlyzko, On conductors and discriminants, in: Algebraic Number Fields: L-functions and Galois Properties, Proc. Sympos., Univ. Durham, Durham 1975, Academic Press, London, 1977, 377-407.
[014] [S-P-D] A. Schwarz, M. Pohst and F. Diaz y Diaz, A table of quintic number fields, Math. Comp. 63 (1994), 361-376. | Zbl 0822.11087
[015] [Sta 1] H. M. Stark, A complete determination of the complex quadratic fields of class-number one, Michigan Math. J. 14 (1967), 1-27.
[016] [Sta 2] H. M. Stark, On complex quadratic fields with class-number two, Math. Comp. 29 (1975), 289-302. | Zbl 0321.12009
[017] [Uch 1] K. Uchida, Imaginary abelian number fields with class number one, Tôhoku Math. J. 24 (1972), 487-499. | Zbl 0248.12007
[018] [Uch 2] K. Uchida, Imaginary abelian number fields of degrees with class number one, in: Class Numbers and Fundamental Units of Algebraic Number Fields, Proc. Internat. Conf. Katata/Jap., 1986, 151-170.
[019] [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Springer, 1982.
[020] [W-B] H. C. Williams and J. Broere, A computational technique for evaluating L(1,χ) and the class number of a real quadratic field, Math. Comp. 30 (1976), 887-893. | Zbl 0345.12004
[021] [Yam] K. Yamamura, The determination of the imaginary abelian number fields with class-number one, Math. Comp. 62 (1994), 899-921. | Zbl 0798.11046