Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20

Acta Arithmetica

Volumn 83, Issue 3, 1998, Pages 211-223

  Park, Young Ho ^a   Kwon, Soun Hi ^a  

^a Korea University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032421928     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa-83-3-211-223     Document Type: Article

References (16)

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3. 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.
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5. _, _, _, _, 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).
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8. F. Lemmermeyer, Ideal class groups of cyclotomic number fields I, Acta Arith. 72 (1995), 347-359.
9. S. Louboutin, CM-fields with cyclic ideal class group of 2-power orders, J. Number Theory, to appear.
10. _, 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.
11. J. Masley and H. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256.
12. B. Setzer, The determination of all imaginary quartic number fields with class number 1, Math. Comp. 35 (1980), 1383-1386.
13. L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983.
14. K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921.
15. 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.
16. _, _, On the relative class number of the imaginary abelian number field II, ibid. 10 (1982), 33-81.