English

Some explicit values of a $q$-multiple zeta function at roots of unity

Number Theory 2025-05-15 v1 Combinatorics

Abstract

In this paper, we give the values of a certain kind of qq-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from generalizations of Stirling numbers. It is interesting, but by no means easy, to show the values explicitly in certain cases. We give explicit formulas by using Bell polynomials, determinants, rr-Stirling numbers, etc.

Keywords

Cite

@article{arxiv.2505.09357,
  title  = {Some explicit values of a $q$-multiple zeta function at roots of unity},
  author = {Takao Komatsu},
  journal= {arXiv preprint arXiv:2505.09357},
  year   = {2025}
}