Determination of all imaginary abelian sextic number fields with class number ≤ 11
Young-Ho Park ; Soun-Hi Kwon
Acta Arithmetica, Tome 80 (1997), p. 27-43 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1997-01-01
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     author = {Young-Ho Park and Soun-Hi Kwon},
     title = {Determination of all imaginary abelian sextic number fields with class number $\leq$ 11},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {27-43},
     zbl = {0889.11036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav82i1p27bwm}
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Young-Ho Park; Soun-Hi Kwon. Determination of all imaginary abelian sextic number fields with class number ≤ 11. Acta Arithmetica, Tome 80 (1997) pp. 27-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav82i1p27bwm/

[000] [A1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334.

[001] [A2] S. Arno, M. L. Robinson and F. S. Wheeler, Imaginary quadratic fields with small odd class number, Algebraic Number Theory Archives, 1993, 1-34; Acta Arith., to appear.

[002] [G.G] G. Gras, Sur les l-classes d'idéaux dans les extensions cycliques relatives de degré premier l, Ann. Inst. Fourier (Grenoble) 23 (3) (1973), 1-48; 23 (4) (1973), 1-44. | Zbl 0276.12013

[003] [M.N.G.] M.-N. Gras, Méthodes et algorithmes pour le calcul numérique du nombre de classes et des unités des extensions cubiques cycliques de ℚ, J. Reine Angew. Math. 277 (1975), 89-116.

[004] [L1] S. Louboutin, Minoration au point 1 des fonctions L et détermination des corps sextiques abéliens totalement imaginaires principaux, Acta Arith. 62 (1992), 109-124.

[005] [L2] S. Louboutin, Majorations explicites de |L(1,χ)|, C. R. Acad. Sci. Paris 316 (1993), 11-14. | Zbl 0774.11051

[006] [L3] S. Louboutin, Lower bounds for relative class numbers of CM-fields, Proc. Amer. Math. Soc. 120 (1994), 425-434. | Zbl 0795.11058

[007] [LO] 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

[008] [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. | Zbl 0893.11045

[009] [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140. | Zbl 0207.05602

[010] [MW] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542. | Zbl 0285.12004

[011] [S1] H. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.

[012] [S2] H. Stark, On complex quadratic fields with class-number two, Math. Comp. 29 (1975), 289-302. | Zbl 0321.12009

[013] [Wg] C. Wagner, Class number 5, 6 and 7, Math. Comp. 65 (1996), 785-800.

[014] [Ws] L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983.

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