Franz Lehner: Sums of cotangents

Sums of powers of cotangents of the form $$ \sum_{k=0}^{n-1} \cot^m\frac{\alpha+k\pi}{n} $$ have been studied in different contexts, like number theory and topology. Recently such sums appeared in our study of a central limit theorem for commutators of random matrices. We give a more or less explicit evaluation of these sums using the trace method in terms of certain integer valued polynomials with positive coefficients, whose combinatorial interpretation remains an open question. This is joint work with W.Ejsmont. The ArXiv link to the paper is: https://arxiv.org/abs/2002.06052