On explicit units in Kummer's tower (Q2122474)

In this article, explicit series of units for two examples of Kummer's towers are constructed, that is, different explicit series of units belonging to the number fields \(K_n =\mathbb{Q}(\sqrt[n]{a})\) (\(n\in\mathbb{N}^*\)), for the cases \(a=2\) and \(a=3\), are given. The author also explains how some of those series of units are consequences of relations existing between values of cyclotomic polynomials. One motivation comes from the study of \(\zeta\)-functions and \(L\)-series in Kummer's towers in [\textit{A. L. Smirnov}, J. Math. Sci., New York 242, No. 4, 568--574 (2019; Zbl 1470.11298); translation from Zap. Nauchn. Semin. POMI 469, 151--159 (2018)].