Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
Young-Ho Park ; Soun-Hi Kwon
Acta Arithmetica, Tome 84 (1998), p. 211-223 / Harvested from The Polish Digital Mathematics Library
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207119
@article{bwmeta1.element.bwnjournal-article-aav83i3p211bwm,
     author = {Young-Ho Park and Soun-Hi Kwon},
     title = {Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number $\leq$ 20},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {211-223},
     zbl = {0895.11047},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav83i3p211bwm}
}
Young-Ho Park; Soun-Hi Kwon. Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20. Acta Arithmetica, Tome 84 (1998) pp. 211-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav83i3p211bwm/

[000] [G] K. Girstmair, The relative class numbers of imaginary cyclic fields of degree 4, 6, 8 and 10, Math. Comp. 61 (1993), 881-887. | Zbl 0787.11046

[001] [M.N.G] M.-N. Gras, Classes et unités des extensions cycliques réelles de degré 4 de ℚ, Ann. Inst. Fourier (Grenoble) 29 (1) (1979), 107-124; Table numérique du nombre de classes et des unités des extensions cycliques réelles de degré 4 de ℚ, Publ. Math. Fac. Sci. Besançon, 1977-78. | Zbl 0387.12001

[002] [HHRW1] K. Hardy, R. H. Hudson, D. Richman and K. Williams, Determination of all imaginary cyclic quartic fields with class number 2, Trans. Amer. Math. Soc. 311 (1989), 1-55. | Zbl 0678.12003

[003] [HHRW2] K. Hardy, R. H. Hudson, D. Richman and K. Williams, Table of the relative class numbers h*(K) of imaginary cyclic quartic fields K with h*(K) ≡ 2 (mod 4) and conductor f < 416,000, Carleton-Ottawa Math. Lecture Note Ser. 8 (1987). | Zbl 0615.12010

[004] [HHRW3] K. Hardy, R. H. Hudson, D. Richman, K. Williams and M. N. Holtz, Calculation of the class numbers of imaginary cyclic quartic fields, Carleton-Ottawa Math. Lecture Note Ser. 7 (1986). | Zbl 0615.12009

[005] [H] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Springer, 1985. | Zbl 0063.01966

[006] [Lm] F. Lemmermeyer, Ideal class groups of cyclotomic number fields I, Acta Arith. 72 (1995), 347-359. | Zbl 0837.11059

[007] [L1] S. Louboutin, CM-fields with cyclic ideal class group of 2-power orders, J. Number Theory, to appear.

[008] [L2] S. Louboutin, Determination of all nonquadratic imaginary cyclic number fields of 2-power degree with ideal class group of exponent ≤ 2, Math. Comp. 64 (1995), 323-340. | Zbl 0822.11072

[009] [MM] J. Masley and H. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256. | Zbl 0335.12013

[010] [S] B. Setzer, The determination of all imaginary quartic number fields with class number 1, Math. Comp. 35 (1980), 1383-1386. | Zbl 0455.12004

[011] [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983. | Zbl 0484.12001

[012] [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921. | Zbl 0798.11046

[013] [YH1] K. Yoshino and M. Hirabayashi, On the relative class number of the imaginary abelian number field I, Mem. College Liberal Arts, Kanazawa Medical Univ. 9 (1981), 5-53.

[014] [YH2] K. Yoshino and M. Hirabayashi, On the relative class number of the imaginary abelian number field II, Kanazawa Medical Univ. 10 (1982), 33-81.