Ideal class groups of cyclotomic number fields I
Acta Arithmetica (1995)
- Volume: 72, Issue: 4, page 347-359
- ISSN: 0065-1036
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topFranz 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
top- [F] B. Ferrero, The cyclotomic ℤ₂-extension of imaginary quadratic number fields, Amer. J. Math. 102 (1980), 447-459. Zbl0463.12002
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- [L] F. Lemmermeyer, Kuroda's class number formula, Acta Arith. 66 (1994), 245-260. Zbl0807.11052
- [Lou] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, J. London Math. Soc., to appear. Zbl0861.11064
- [LOO] S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, preprint, 1994.
- [M] T. Metsänkylä, Über den ersten Faktor der Klassenzahl des Kreiskörpers, Ann. Acad. Sci. Fenn. Ser. A I 416, 1967.
- [MM] J. M. Masley and H. L. Montgomery, Cyclotomic fields with unique factorization, J. Reine Angew. Math. 286/287 (1976), 248-256. Zbl0335.12013
- [O] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153. Zbl0776.11071
- [S] A. Scholz, Über die Lösbarkeit der Gleichung t² - Du² = -4, Math. Z. 39 (1934), 95-111. Zbl0009.29402
- [U] K. Uchida, Imaginary quadratic number fields with class number one, Tôhoku Math. J. 24 (1972), 487-499. Zbl0248.12007
- [W] L. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982. Zbl0484.12001
- [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
top- Young-Ho Park, Soun-Hi Kwon, Determination of all non-quadratic imaginary cyclic number fields of 2-power degree with relative class number ≤ 20
- Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, On some imaginary triquadratic number fields with or
- F. Lemmermeyer, S. Louboutin, R. Okazaki, The class number one problem for some non-abelian normal CM-fields of degree
- Franz Lemmermeyer, Ideal class groups of cyclotomic number fields II
- Yasushi Mizusawa, On the maximal unramified pro-2-extension over the cyclotomic -extension of an imaginary quadratic field
- Ryotaro Okazaki, Inclusion of CM-fields and divisibility ofrelative class numbers
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