A table of fundamental pairs of units in totally real cubic fields

Cusick, T. W.; Schoenfeld, Lowell

doi:10.1090/S0025-5718-1987-0866105-8

A table of fundamental pairs of units in totally real cubic fields
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by T. W. Cusick and Lowell Schoenfeld PDF

Math. Comp. 48 (1987), 147-158 Request permission

Abstract:

We apply a method of Cusick [5] to tabulate data on the first 250 totally real cubic fields F having discriminant $D \leqslant 6,885$. Apart from D, we list the class number H and the regulator R of F. Also given are the integer coefficients A,B,C of a defining polynomial $g(x) = {x^3} - A{x^2} + Bx - C$, its index I, and its largest zero ${R_0}$. For $j = 1,2$, we also tabulate both the integer coefficients ${X_j},{Y_j},{Z_j}$ for the two units ${E_j} = ({X_j} + {R_0}{Y_j} + R_0^2{Z_j})/I$ with norm $+ 1$, forming a fundamental pair, as well as the ${E_j}$ and the integers ${F_j} = {\text {trace}}(E_j^2)$.

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On a Generalization of the Algorithm for Continued Fractions

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