Character coordinates and annihilators of cyclotomic numbers (Q1092111)

``The object of this paper is a representation theoretical approach to the problem of determining all \({\mathbb{Q}}\)-linear relations between conjugate numbers in a cyclotomic field.'' It is based on the `character coordinates' of numbers in an abelian number field introduced by \textit{H.- W. Leopoldt} [J. Reine Angew. Math. 201, 119-149 (1959; Zbl 0098.034)]. ``We apply our method to relations between the numbers \(\cot^{(m)}(\pi k/n)\), \(\tan^{(m)}(\pi k/n)\), \(\cos ec^{(m)}(2\pi k/n)\), \(\sec^{(m)}(2\pi k/n)\), respectively, where m is \(\geq 0\) and \((k,n)=1\). Thereby we complete work of Chowla, Hasse, Jager-Lenstra, and others.''