Class numbers and units of E. Lehmer's cyclic quintic fields
In her article `Connection between Gaussian periods and cyclic units' [Math. Comput. 50, 535-541 (1988; Zbl 0652.12004)], \textit{E. Lehmer} introduced a parametrized family of quintic polynomials \(P_t\) whose roots generate a subgroup of finite index in the unit group of the corresponding cyclic quintic field. In the article under review, the author proves that these units are fundamental if the discriminant of the polynomial satisfies a certain condition (this generalizes previous results of \textit{R. Schoof} and \textit{L. C. Washington} [Math. Comput. 50, 543-556 (1988; Zbl 0649.12007)]), and computes the ideal class groups of the fields for small values of \(t\) and conductor \(<3 \cdot 10^6\). This is done by first computing the group of cyclotomic units, and then checking which of the units in this group are powers of units in the field.
scientific article; zbMATH DE number 912499