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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  1. S. Bosca, Comparing orders of Selmer groups. Jour. Théo. Nomb. Bordeaux 17 (2005), 467–473. Zbl1098.11056MR2211302
  2. H. Cohen, Advanced Topics in Computational Number Theory, Graduate Texts in Math. 193, Springer-Verlag, 2000. Zbl0977.11056MR1728313
  3. H. Cohen, High precision computation of Hardy–Littlewood constants, preprint available on the author’s web page. 
  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
  7. H. Cohen, F. Diaz y Diaz, M. Olivier, Counting discriminants of number fields, submitted. Zbl1193.11109
  8. B. Datskovsky, D. J. Wright, Density of discriminants of cubic extensions, J. reine angew. Math. 386 (1988), 116–138. Zbl0632.12007MR936994
  9. J. Klüners, A counter-example to Malle’s conjecture on the asymptotics of discriminants, C. R. Acad. Sci. Paris 340 (2005), 411–414. Zbl1083.11069
  10. S. Mäki, On the density of abelian number fields, Thesis, Helsinki, 1985. Zbl0566.12001MR791087
  11. S. Mäki, The conductor density of abelian number fields, J. London Math. Soc. (2) 47 (1993), 18–30. Zbl0727.11041MR1200974
  12. G. Malle, On the distribution of Galois groups, J. Number Th. 92 (2002), 315–329. Zbl1022.11058MR1884706
  13. G. Malle, On the distribution of Galois groups II, Exp. Math. 13 (2004), 129–135. Zbl1099.11065MR2068887
  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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