Counting cyclic quartic extensions of a number field

Henri Cohen; Francisco Diaz y Diaz; Michel Olivier[1]

  • [1] Henri Cohen, Francisco Diaz y Diaz et Michel Olivier Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 TALENCE Cedex, FRANCE

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 475-510
  • ISSN: 1246-7405

Abstract

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In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.

How to cite

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Cohen, Henri, Diaz y Diaz, Francisco, and Olivier, Michel. "Counting cyclic quartic extensions of a number field." Journal de Théorie des Nombres de Bordeaux 17.2 (2005): 475-510. <http://eudml.org/doc/249445>.

@article{Cohen2005,
abstract = {In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.},
affiliation = {Henri Cohen, Francisco Diaz y Diaz et Michel Olivier Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 TALENCE Cedex, FRANCE},
author = {Cohen, Henri, Diaz y Diaz, Francisco, Olivier, Michel},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {density; discriminants; cyclic quartic extensions; ramification},
language = {eng},
number = {2},
pages = {475-510},
publisher = {Université Bordeaux 1},
title = {Counting cyclic quartic extensions of a number field},
url = {http://eudml.org/doc/249445},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Cohen, Henri
AU - Diaz y Diaz, Francisco
AU - Olivier, Michel
TI - Counting cyclic quartic extensions of a number field
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 475
EP - 510
AB - In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.
LA - eng
KW - density; discriminants; cyclic quartic extensions; ramification
UR - http://eudml.org/doc/249445
ER -

References

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  4. H. Cohen, F. Diaz y Diaz, M. Olivier, On the density of discriminants of cyclic extensions of prime degree, J. reine angew. Math. 550 (2002), 169–209. Zbl1004.11063MR1925912
  5. H. Cohen, F. Diaz y Diaz, M. Olivier, Cyclotomic extensions of number fields, Indag. Math. (N.S.) 14 (2003), 183–196. Zbl1056.11058MR2026813
  6. H. Cohen, F. Diaz y Diaz, M. Olivier, Counting biquadratic extensions of a number field, preprint. Zbl1090.11068
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  12. G. Malle, On the distribution of Galois groups, J. Number Th. 92 (2002), 315–329. Zbl1022.11058MR1884706
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  14. D. J. Wright, Distribution of discriminants of Abelian extensions, Proc. London Math. Soc. (3) 58 (1989), 17–50. Zbl0628.12006MR969545

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