On CM-fields with the same maximal real subfield

Kuniaki Horie

Acta Arithmetica (1994)

  • Volume: 67, Issue: 3, page 219-227
  • ISSN: 0065-1036

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Kuniaki Horie. "On CM-fields with the same maximal real subfield." Acta Arithmetica 67.3 (1994): 219-227. <http://eudml.org/doc/206628>.

@article{KuniakiHorie1994,
author = {Kuniaki Horie},
journal = {Acta Arithmetica},
keywords = {CM-field; Iwasawa invariants; totally real number field; totally imaginary quadratic extensions; odd relative class number},
language = {eng},
number = {3},
pages = {219-227},
title = {On CM-fields with the same maximal real subfield},
url = {http://eudml.org/doc/206628},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Kuniaki Horie
TI - On CM-fields with the same maximal real subfield
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 3
SP - 219
EP - 227
LA - eng
KW - CM-field; Iwasawa invariants; totally real number field; totally imaginary quadratic extensions; odd relative class number
UR - http://eudml.org/doc/206628
ER -

References

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  1. [1] B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math. 386 (1988), 116-138. Zbl0632.12007
  2. [2] H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, II, Proc. Roy. Soc. London Ser. A 322 (1971), 405-420. Zbl0212.08101
  3. [3] E. Friedman, Iwasawa invariants, Math. Ann. 271 (1985), 13-30. Zbl0533.12007
  4. [4] H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Phisica-Verlag, Würzburg-Wien, 1970. 
  5. [5] K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38. 
  6. [6] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258. Zbl0074.03002
  7. [7] Y. Kida, Cyclotomic ℤ₂-extensions of J-fields, J. Number Theory 14 (1982), 340-352. 
  8. [8] T. Kubota, Über den bizyklischen biquadratischen Zahlkörper, Nagoya Math. J. 10 (1956), 65-85. Zbl0074.03001
  9. [9] H. Naito, Indivisibility of class numbers of totally imaginary quadratic extensions and their Iwasawa invariants, J. Math. Soc. Japan 43 (1991), 185-194. Zbl0719.11072
  10. [10] J. Nakagawa and K. Horie, Elliptic curves with no rational points, Proc. Amer. Math. Soc. 104 (1988), 20-24. Zbl0663.14023
  11. [11] L. Rédei and H. Reichardt, Die Anzahl der durch 4 teilbaren Invarianten der Klassengruppe eines beliebigen quadratischen Zahlkörpers, J. Reine Angew. Math. 170 (1933), 69-74. Zbl59.0192.01
  12. [12] L. C. Washington, Introduction to Cyclotomic Fields, Springer, New York, 1982. Zbl0484.12001

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