Berger, Arno On linear independence of trigonometric numbers. (English) Zbl 1449.11078 Carpathian J. Math. 34, No. 2, 157-166 (2018). Summary: A necessary and sufficient condition is established for 1, cos\((\pi r_1)\), and cos\((\pi r_2)\) to be rationally independent, where \(r_1, r_2\) are rational numbers. The elementary computational argument yields linear independence over larger number fields as well. Cited in 2 Documents MSC: 11J72 Irrationality; linear independence over a field 11R11 Quadratic extensions Keywords:Niven’s Theorem; trigonometric number; rational (in)dependence; cyclotomic polynomial; real quadratic number field PDFBibTeX XMLCite \textit{A. Berger}, Carpathian J. Math. 34, No. 2, 157--166 (2018; Zbl 1449.11078) Full Text: arXiv