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Uniformity over primes of unramified splittings

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 February 2010

Ilaria Del Corso  and
Roberto Dvornicich
Ilaria Del Corso
Affiliation:
Dipartimento di Matematica, via Buonarroti, 2, 56127, Pisa, Italy. e-mail: [email protected]
Roberto Dvornicich
Affiliation:
Dipartimento di Matematica, via Buonarroti, 2, 56127, Pisa, Italy. e-mail: [email protected]
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Extract

The following theorem, due to Artin [1], is one of a number of statements often referred to as Chebotarev density theorem.

MSC classification

Secondary: 11R45: Density theorems
Type
Research Article
Information
Mathematika , Volume 45 , Issue 1 , June 1998 , pp. 177 - 189
Copyright
Copyright © University College London 1998

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References

1.Artin, E.. Über die Zetafunktionen gewisser algebraischer Zahlkörper. Math. Ann., 89 (1923), 147–156.CrossRefGoogle Scholar
2.Davenport, H. and Heilbronn, H.. On the density of discriminants of cubic fields II. Proc. Roy. Soc. London, 332 (1971), 405–420.Google Scholar
3.Del Corso, I. and Dvornicich, R.. A converse of Artin's density theorem: the case of cubic fields. J. Number Theory, 45 (1993), 28–44.Google Scholar
4.Koblitz, N.. p-adic Numbers, p-adic Analysis and Zeta-Functions, Second Edition (Springer Verlag, 1984).CrossRefGoogle Scholar
5.Narkiewicz, W.. Elementary and Analytic Theory of Algebraic Numbers, Second Edition (Springer Verlag, 1990).Google Scholar
6.Ore, O.. Über den Zusammenhang zwischen den delinierenden Gleichungen und der Idealtheorie in algebraishen Körpern. Math. Ann., 96 (1927), 313–352.CrossRefGoogle Scholar
7.Taylor, M. J.. On the equidistribution of Frobenius in cyclic extensions of a number field. J. London Math. Soc., 29 (1984), 211[223.CrossRefGoogle Scholar
8.van der Ploeg, C. E.. On a converse to the Tschebotarev density theorem. J. Austral. Math. Soc., 44 (1988), 287–293.CrossRefGoogle Scholar
9.Weil, A.. Adeles and Algebraic Groups (Birkhäuser, 1982).CrossRefGoogle Scholar