On the number of certain Galois extensions of local fields
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- by Da-sheng Wei and Chun-gang Ji PDF
- Proc. Amer. Math. Soc. 135 (2007), 3041-3047 Request permission
Abstract:
In this paper, we will calculate the number of Galois extensions of local fields with Galois group $A_n$ or $S_n$.References
- Marc Krasner, Nombre des extensions d’un degré donné d’un corps ${\mathfrak {p}}$-adique, Les Tendances Géom. en Algèbre et Théorie des Nombres, Éditions du Centre National de la Recherche Scientifique (CNRS), Paris, 1966, pp. 143–169 (French). MR 0225756
- Serge Lang, Algebraic number theory, 2nd ed., Graduate Texts in Mathematics, vol. 110, Springer-Verlag, New York, 1994. MR 1282723, DOI 10.1007/978-1-4612-0853-2
- Sebastian Pauli and Xavier-François Roblot, On the computation of all extensions of a $p$-adic field of a given degree, Math. Comp. 70 (2001), no. 236, 1641–1659. MR 1836924, DOI 10.1090/S0025-5718-01-01306-0
- I. Shafarevitch, On $p$-extensions, Rec. Math. [Mat. Sbornik] N.S. 20(62) (1947), 351–363 (Russian, with English summary). MR 0020546
- Jean-Pierre Serre, Corps locaux, Publications de l’Université de Nancago, No. VIII, Hermann, Paris, 1968 (French). Deuxième édition. MR 0354618
- Jean-Pierre Serre, Une “formule de masse” pour les extensions totalement ramifiées de degré donné d’un corps local, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 22, A1031–A1036 (French, with English summary). MR 500361
- Masakazu Yamagishi, On the number of Galois $p$-extensions of a local field, Proc. Amer. Math. Soc. 123 (1995), no. 8, 2373–2380. MR 1264832, DOI 10.1090/S0002-9939-1995-1264832-0
Additional Information
- Da-sheng Wei
- Affiliation: Department of Mathematics, the University of Science and Technology of China, Hefei, People’s Republic of China 230026
- Email: dshwei@ustc.edu
- Chun-gang Ji
- Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing, People’s Republic of China 210097
- Email: cgji@njnu.edu.cn
- Received by editor(s): June 13, 2006
- Published electronically: May 10, 2007
- Additional Notes: This work was partially supported by grants #10171046 and #10201013 from NNSF of China and Jiangsu planned projects for postdoctoral research funds
- Communicated by: Ken Ono
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3041-3047
- MSC (2000): Primary 11S15, 11S20
- DOI: https://doi.org/10.1090/S0002-9939-07-08905-8
- MathSciNet review: 2322733