Ideal class groups of cyclotomic number fields I

Franz Lemmermeyer

Acta Arithmetica (1995)

  • Volume: 72, Issue: 4, page 347-359
  • ISSN: 0065-1036

How to cite

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Franz Lemmermeyer. "Ideal class groups of cyclotomic number fields I." Acta Arithmetica 72.4 (1995): 347-359. <http://eudml.org/doc/206801>.

@article{FranzLemmermeyer1995,
author = {Franz Lemmermeyer},
journal = {Acta Arithmetica},
keywords = {cyclotomic fields; CM-fields; totally complex quadratic extensions; unit index; relative class number; capitulation; Hilbert class fields},
language = {eng},
number = {4},
pages = {347-359},
title = {Ideal class groups of cyclotomic number fields I},
url = {http://eudml.org/doc/206801},
volume = {72},
year = {1995},
}

TY - JOUR
AU - Franz Lemmermeyer
TI - Ideal class groups of cyclotomic number fields I
JO - Acta Arithmetica
PY - 1995
VL - 72
IS - 4
SP - 347
EP - 359
LA - eng
KW - cyclotomic fields; CM-fields; totally complex quadratic extensions; unit index; relative class number; capitulation; Hilbert class fields
UR - http://eudml.org/doc/206801
ER -

References

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  1. [F] B. Ferrero, The cyclotomic ℤ₂-extension of imaginary quadratic number fields, Amer. J. Math. 102 (1980), 447-459. Zbl0463.12002
  2. [H] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Springer, Berlin, 1985. 
  3. [HY] M. Hirabayashi and K. Yoshino, Remarks on unit indices of imaginary abelian number fields, Manuscripta Math. 60 (1988), 423-436. Zbl0654.12002
  4. [Ho] K. Horie, On a ratio between relative class numbers, Math. Z. 211 (1992), 505-521. Zbl0761.11039
  5. [L] F. Lemmermeyer, Kuroda's class number formula, Acta Arith. 66 (1994), 245-260. Zbl0807.11052
  6. [Lou] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, J. London Math. Soc., to appear. Zbl0861.11064
  7. [LOO] S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, preprint, 1994. 
  8. [M] T. Metsänkylä, Über den ersten Faktor der Klassenzahl des Kreiskörpers, Ann. Acad. Sci. Fenn. Ser. A I 416, 1967. 
  9. [MM] J. M. Masley and H. L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256. Zbl0335.12013
  10. [O] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153. Zbl0776.11071
  11. [S] A. Scholz, Über die Lösbarkeit der Gleichung t² - Du² = -4, Math. Z. 39 (1934), 95-111. Zbl0009.29402
  12. [U] K. Uchida, Imaginary quadratic number fields with class number one, Tôhoku Math. J. 24 (1972), 487-499. Zbl0248.12007
  13. [W] L. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982. Zbl0484.12001
  14. [We] J. Westlund, On the class number of the cyclotomic number field, Trans. Amer. Math. Soc. 4 (1903), 201-212. Zbl34.0237.02

Citations in EuDML Documents

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  1. Young-Ho Park, Soun-Hi Kwon, Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
  2. F. Lemmermeyer, S. Louboutin, R. Okazaki, The class number one problem for some non-abelian normal CM-fields of degree 24
  3. Franz Lemmermeyer, Ideal class groups of cyclotomic number fields II
  4. Yasushi Mizusawa, On the maximal unramified pro-2-extension over the cyclotomic 2 -extension of an imaginary quadratic field
  5. Ryotaro Okazaki, Inclusion of CM-fields and divisibility ofrelative class numbers

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