# Franz Lehner: Sums of cotangents

Date of publication: 10. 1. 2022

Algebra and functional analysis seminar

Thursday

13

January

Time:

12:30 - 13:30

Location:

Zoom

ID: 969 9112 4526
–
Password: 065342

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

Vljudno vabljeni!

Roman Drnovšek in Primož Moravec