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A numerical study of the relative class numbers of real quadratic integral domains


Author: Harvey Cohn
Journal: Math. Comp. 16 (1962), 127-140
MSC: Primary 10.66
DOI: https://doi.org/10.1090/S0025-5718-1962-0144885-X
MathSciNet review: 0144885
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  • [1] H. Cohn, ``A numerical study of Dedekind's cubic class number formula,'' J. Res. Nat. Bur. Standards, v. 59, 1957, p. 265-271. (A similar composition problem is treated on a computer here.) MR 0091308 (19:944a)
  • [2] E. C. Dade, O. Taussky, & H. Zassenhaus, ``On the semi-group of ideal classes in an order of an algebraic number field,'' Bull. Amer. Math. Soc., v. 67, 1961, p. 305-308. (The ideals which divide f, normally excluded from class number considerations, are treated theoretically and with the aid of computers.) MR 0136597 (25:65)
  • [3] R. Dedekind, ``Über die Anzahl der Idealklassen in reinen kübischer Zahlkörpern,'' J. Reine Angew. Math., v. 121, 1900, p. 40-123.
  • [4] P. G. L. Dirichlet, ``Une propriete des formes quadratiques a determinant positive,'' J. Math. Pures Appl. Ser II, v. 1, 1856, p. 76-79.
  • [5] R. Fueter, Vorlesungen über die singulären Moduln und die komplexe Multiplikation der elliptischen Funktionen, v. 1, II Leipzig-Berlin, 1924. (This work gives the classic application of relative class structures concisely.)
  • [6] H. Hasse, ``Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage,'' Math Z. v. 31, 1929, p. 565-582. (Reference centers primarily on the top line of the table on p. 568.) MR 1545136
  • [7] H. Weber, Lehrbuch der Algebra, v. II, III, Braunschweig, 1894, 1908.
  • [8] H. Weber, ``Beweiss des Satzes dass jede eigentliche primitive quadratische Form unendlich viele Primzahlen darstellen fähig ist,'' Math. Ann, v. 20, 1882, p. 301-329. MR 1510171

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DOI: https://doi.org/10.1090/S0025-5718-1962-0144885-X
Article copyright: © Copyright 1962 American Mathematical Society

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