The trace method for cotangent sums

Wiktor Ejsmont*, Franz Lehner

*Korrespondierende/r Autor/in für diese Arbeit

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

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.

Originalspracheenglisch
Aufsatznummer105324
FachzeitschriftJournal of Combinatorial Theory. Series A
Jahrgang177
DOIs
PublikationsstatusVeröffentlicht - Jan 2021

ASJC Scopus subject areas

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

Fingerprint Untersuchen Sie die Forschungsthemen von „The trace method for cotangent sums“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren