TY - JOUR
T1 - The density of discriminants of S3-sextic number fields
AU - Bhargava, Manjul
AU - Wood, Melanie Matchett
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2008/5
Y1 - 2008/5
N2 - We prove an asymptotic formula for the number of sextic number fields with Galois group S3 and absolute discriminant <X. In addition, we give an interpretation of the constant in the formula in terms of the asymptotic densities of given local completions among these sextic fields. Our proof gives analogous results when we count S3-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.
AB - We prove an asymptotic formula for the number of sextic number fields with Galois group S3 and absolute discriminant <X. In addition, we give an interpretation of the constant in the formula in terms of the asymptotic densities of given local completions among these sextic fields. Our proof gives analogous results when we count S3-sextic extensions of any number field, and also when finitely many local completions have been specified for the sextic extensions.
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U2 - 10.1090/S0002-9939-07-09171-X
DO - 10.1090/S0002-9939-07-09171-X
M3 - Article
AN - SCOPUS:77950647952
VL - 136
SP - 1581
EP - 1587
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 5
ER -