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Mathematics of Computation

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

Authors: T. W. Cusick and Lowell Schoenfeld
Journal: Math. Comp. 48 (1987), 147-158
MSC: Primary 11R27; Secondary 11Y40
MathSciNet review: 866105
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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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Article copyright: © Copyright 1987 American Mathematical Society