Determination of all imaginary abelian sextic number fields with class number ≤ 11

• Autorzy: Young-Ho Park , Soun-Hi Kwon
• Języki publikacji: EN

Kategorie tematyczne

• 11R20: Other abelian and metabelian extensions
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 1
• Strony: 27-43

Daty

wydano

1997

otrzymano

1996-05-25

poprawiono

1997-02-18

Twórcy

autor

Young-Ho Park

• Department of Mathematics, Korea University, 136-701 Seoul, Korea

autor

Soun-Hi Kwon

• Department of Mathematics Education, Korea University, 136-701, Seoul, Korea

Bibliografia

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• [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.
• [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.
• [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.
• [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.
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• [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.
• [Low] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arith. 14 (1968), 117-140.
• [MW] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542.
• [S1] H. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.
• [S2] H. Stark, On complex quadratic fields with class-number two, Math. Comp. 29 (1975), 289-302.
• [Wg] C. Wagner, Class number 5, 6 and 7, Math. Comp. 65 (1996), 785-800.
• [Ws] L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983.
• [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921.