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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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?)

  • [1] A. I. Borevich and I. R. Shafarevich, Number theory, Translated from the Russian by Newcomb Greenleaf. Pure and Applied Mathematics, Vol. 20, Academic Press, New York-London, 1966. MR 0195803 (33 #4001)
  • [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 (84c:12002), http://dx.doi.org/10.1515/crll.1982.337.195
  • [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 (50 #12967)
  • [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 (2,147a)
  • [6] L. Rédei, "Über einige Mittelwertfragen im quadratischen Zahlkörper," J. Reine Angew. Math., v. 174, 1936, pp. 15-55.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0701637-0
PII: S 0025-5718(1983)0701637-0
Article copyright: © Copyright 1983 American Mathematical Society