In this paper, we give asymptotic formulas for the number of cyclic quartic extensions of a number field.
Nous donnons des formules asymptotiques pour le nombre d’extensions cycliques quartiques d’un corps de nombres général.
Cohen, Henri ; Diaz y Diaz, Francisco ; Olivier, Michel 1
@article{JTNB_2005__17_2_475_0,
author = {Cohen, Henri and Diaz y Diaz, Francisco and Olivier, Michel},
title = {Counting cyclic quartic extensions of a number field},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {475--510},
year = {2005},
publisher = {Universit\'e Bordeaux 1},
volume = {17},
number = {2},
doi = {10.5802/jtnb.503},
zbl = {1090.11068},
mrnumber = {2211303},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.503/}
}
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 SP - 475 EP - 510 VL - 17 IS - 2 PB - Université Bordeaux 1 UR - https://www.numdam.org/articles/10.5802/jtnb.503/ DO - 10.5802/jtnb.503 LA - en ID - JTNB_2005__17_2_475_0 ER -
%0 Journal Article %A Cohen, Henri %A Diaz y Diaz, Francisco %A Olivier, Michel %T Counting cyclic quartic extensions of a number field %J Journal de théorie des nombres de Bordeaux %D 2005 %P 475-510 %V 17 %N 2 %I Université Bordeaux 1 %U https://www.numdam.org/articles/10.5802/jtnb.503/ %R 10.5802/jtnb.503 %G en %F JTNB_2005__17_2_475_0
Cohen, Henri; Diaz y Diaz, Francisco; Olivier, Michel. Counting cyclic quartic extensions of a number field. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 475-510. doi: 10.5802/jtnb.503
[1] S. Bosca, Comparing orders of Selmer groups. Jour. Théo. Nomb. Bordeaux 17 (2005), 467–473. | Zbl | MR | Numdam
[2] H. Cohen, Advanced Topics in Computational Number Theory, Graduate Texts in Math. 193, Springer-Verlag, 2000. | Zbl | MR
[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. | Zbl | MR
[5] H. Cohen, F. Diaz y Diaz, M. Olivier, Cyclotomic extensions of number fields, Indag. Math. (N.S.) 14 (2003), 183–196. | Zbl | MR
[6] H. Cohen, F. Diaz y Diaz, M. Olivier, Counting biquadratic extensions of a number field, preprint.
[7] H. Cohen, F. Diaz y Diaz, M. Olivier, Counting discriminants of number fields, submitted.
[8] B. Datskovsky, D. J. Wright, Density of discriminants of cubic extensions, J. reine angew. Math. 386 (1988), 116–138. | Zbl | MR
[9] J. Klüners, A counter-example to Malle’s conjecture on the asymptotics of discriminants, C. R. Acad. Sci. Paris 340 (2005), 411–414. | Zbl
[10] S. Mäki, On the density of abelian number fields, Thesis, Helsinki, 1985. | Zbl | MR
[11] S. Mäki, The conductor density of abelian number fields, J. London Math. Soc. (2) 47 (1993), 18–30. | Zbl | MR
[12] G. Malle, On the distribution of Galois groups, J. Number Th. 92 (2002), 315–329. | Zbl | MR
[13] G. Malle, On the distribution of Galois groups II, Exp. Math. 13 (2004), 129–135. | Zbl | MR
[14] D. J. Wright, Distribution of discriminants of Abelian extensions, Proc. London Math. Soc. (3) 58 (1989), 17–50. | Zbl | MR
Cité par Sources :
