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 (1998)

  • Volume: 83, Issue: 3, page 211-223
  • ISSN: 0065-1036

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Young-Ho Park, and Soun-Hi Kwon. "Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20." Acta Arithmetica 83.3 (1998): 211-223. <http://eudml.org/doc/207119>.

@article{Young1998,
author = {Young-Ho Park, Soun-Hi Kwon},
journal = {Acta Arithmetica},
keywords = {imaginary cyclic number fields; relative class number; upper bounds for conductors},
language = {eng},
number = {3},
pages = {211-223},
title = {Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20},
url = {http://eudml.org/doc/207119},
volume = {83},
year = {1998},
}

TY - JOUR
AU - Young-Ho Park
AU - Soun-Hi Kwon
TI - Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
JO - Acta Arithmetica
PY - 1998
VL - 83
IS - 3
SP - 211
EP - 223
LA - eng
KW - imaginary cyclic number fields; relative class number; upper bounds for conductors
UR - http://eudml.org/doc/207119
ER -

References

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  1. [G] K. Girstmair, The relative class numbers of imaginary cyclic fields of degree 4, 6, 8 and 10, Math. Comp. 61 (1993), 881-887. Zbl0787.11046
  2. [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. Zbl0387.12001
  3. [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. Zbl0678.12003
  4. [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). Zbl0615.12010
  5. [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). Zbl0615.12009
  6. [H] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Springer, 1985. Zbl0063.01966
  7. [Lm] F. Lemmermeyer, Ideal class groups of cyclotomic number fields I, Acta Arith. 72 (1995), 347-359. Zbl0837.11059
  8. [L1] S. Louboutin, CM-fields with cyclic ideal class group of 2-power orders, J. Number Theory, to appear. 
  9. [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. Zbl0822.11072
  10. [MM] J. Masley and H. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256. Zbl0335.12013
  11. [S] B. Setzer, The determination of all imaginary quartic number fields with class number 1, Math. Comp. 35 (1980), 1383-1386. Zbl0455.12004
  12. [W] L. C. Washington, Introduction to Cyclotomic Fields, Springer, 1983. Zbl0484.12001
  13. [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), 899-921. Zbl0798.11046
  14. [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. 
  15. [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. 

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