The trace method for cotangent sums

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:177

Article

Ejsmont, Wiktor¹  Lehner, Franz² 

[1] Uniwersytet Wroclawski, Inst Matemat, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[2] Graz Univ Technol, Inst Diskrete Math, Steyrergasse 30, A-8010 Graz, Austria

关键词: Trigonometric power sum;    Integer valued polynomials;    Higher tangent numbers;    Derivative polynomials;    Combinatorial identities;   

DOI  :  10.1016/j.jcta.2020.105324

来源: Elsevier

【 摘 要 】

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. (C) 2020 The Authors. Published by Elsevier Inc.

【 授权许可】

Free