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October 9, 2025Open Access

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

Key Points

Explicit formulas for certain q-multiple zeta functions are demonstrated using advanced combinatorial tools.
The research uncovers values at roots of unity, emphasizing their relation to Stirling numbers and combinatorial structures.
Bell polynomials and determinants are utilized to provide clear and insightful representations of these values.
The findings indicate unique properties of multiple zeta functions, highlighting their complexity and significance in mathematical research.

Abstract

In this paper, we give the values of a certain kind of q-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, r-Stirling numbers, etc.

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Cite This Study

Takao Komatsu (Wed,) studied this question.

synapsesocial.com/papers/68e8439a9989581a2fd4df76 https://doi.org/https://doi.org/10.48550/arxiv.2505.09357

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