The trace method for cotangent sums

Wiktor Ejsmont*, Franz Lehner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents a combinatorial study of sums of integer powers of the cotangent. Our main tool is the realization of the cotangent values as eigenvalues of a simple self-adjoint matrix with complex integer entries. We use the trace method to draw conclusions about integer values of the sums and series expansions of the generating function to provide explicit evaluations; it is remarkable that throughout the calculations the combinatorics are governed by the higher tangent and arctangent numbers exclusively. Finally, we indicate a new approximation of the values of the Riemann zeta function at even integer arguments.

Original languageEnglish
Article number105324
JournalJournal of Combinatorial Theory, Series A
Publication statusPublished - Jan 2021


  • Combinatorial identities
  • Derivative polynomials
  • Higher tangent numbers
  • Integer valued polynomials
  • Trigonometric power sum

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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