An application of matrices over finite fields to algebraic number theory
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- by Frank Gerth PDF
- Math. Comp. 41 (1983), 229-234 Request permission
Abstract:
This paper ultilizes properties of matrices over finite fields to obtain information about the rank of the p-class group of certain algebraic number fields.References
- A. I. Borevich and I. R. Shafarevich, Number theory, Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. Translated from the Russian by Newcomb Greenleaf. MR 0195803 F. Gerth, "Consequences of l-th power reciprocity." (To appear.)
- Frank Gerth III, Counting certain number fields with prescribed $l$-class numbers, J. Reine Angew. Math. 337 (1982), 195–207. MR 676052, DOI 10.1515/crll.1982.337.195
- Georges Gras, Sur les $l$-classes d’idéaux dans les extensions cycliques relatives de degré premier $l$. I, II, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 3, 1–48; ibid. 23 (1973), no. 4, 1–44 (French, with English summary). MR 360519, DOI 10.5802/aif.471
- Eizi Inaba, Über die Struktur der $l$-Klassengruppe zyklischer Zahlkörper vom Primzahlgrad $l$, J. Fac. Sci. Imp. Univ. Tokyo Sect. I. 4 (1940), 61–115 (German). MR 0002999 L. Rédei, "Über einige Mittelwertfragen im quadratischen Zahlkörper," J. Reine Angew. Math., v. 174, 1936, pp. 15-55.
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 229-234
- MSC: Primary 11R29; Secondary 11R21, 15A33
- DOI: https://doi.org/10.1090/S0025-5718-1983-0701637-0
- MathSciNet review: 701637