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An application of matrices over finite fields to algebraic number theory

Author: Frank Gerth
Journal: Math. Comp. 41 (1983), 229-234
MSC: Primary 11R29; Secondary 11R21, 15A33
MathSciNet review: 701637
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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 [Enhancements On Off] (What's this?)

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  • [2] F. Gerth, "Consequences of l-th power reciprocity." (To appear.)
  • [3] Frank Gerth III, Counting certain number fields with prescribed 𝑙-class numbers, J. Reine Angew. Math. 337 (1982), 195–207. MR 676052,
  • [4] 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 0360519
  • [5] 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
  • [6] L. Rédei, "Über einige Mittelwertfragen im quadratischen Zahlkörper," J. Reine Angew. Math., v. 174, 1936, pp. 15-55.

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Article copyright: © Copyright 1983 American Mathematical Society

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