## Dirichlet series associated to cubic fields with given quadratic resolvent

*Cohen, Henri*;

*Thorne, Frank*;

- Publisher: University of Michigan
- Journal: issn: 0026-2285
Related identifiers: doi: 10.1307/mmj/1401973050 - Subject: 11R29 | [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT] | 11R37 | 11R16 | Mathematics - Number Theory | 11Y40

- References (20) 20 references, page 1 of 2
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[1] J. Armitage and A. Fr¨ohlich, Class numbers and unit signatures, Mathematika 14 (1967), 94-98.

[2] K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), no. 219, 1213-1237; accompanying software available at http://www.math.u-bordeaux1.fr/~belabas/research/software/cubic-1.2.tgz.

[3] M. Bhargava, The density of discriminants of quartic rings and fields, Ann. of Math. (2) 162 (2005), no. 2, 1031-1063.

[4] M. Bhargava, Mass formulae for extensions of local fields, and conjectures on the density of number field discriminants, Int. Math. Res. Not. (2007), no. 17, Art. ID rnm052, 20 pp.

[5] M. Bhargava, Higher composition laws and applications, Proceedings of the International Congress of Mathematicians, Vol. II, 271294, Eur. Math. Soc., Zu¨rich, 2006.

[6] M. Bhargava, The density of discriminants of quintic rings and fields, Ann. Math. (2) 172 (2010), no. 3, 1559- 1591.

[7] M. Bhargava, A. Shankar, and J. Tsimerman, On the Davenport-Heilbronn theorem and second order terms, preprint; available at http://arxiv.org/abs/1005.0672

[8] H. Cohen, F. Diaz y Diaz, and M. Olivier, Counting discriminants of number fields, J. Th´eor. Nombres Bordeaux 18 (2006), no. 3, 573-593.

[9] H. Cohen and A. Morra, Counting cubic extensions with given quadratic resolvent, J. Algebra 325 (2011), 461- 478. (Theorem numbers refer to the published version, which are different than in the arXiv version.)

[10] H. Cohn, The density of abelian cubic fields, Proc. Amer. Math. Soc. 5 (1954), 476-477.

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