January 1, 2025RAIRO - Theoretical Informatics and ApplicationsOpen Access

Explicit values of a q-multiple zeta-star function at roots of unity

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Explicit formulas for q-multiple zeta-star functions at roots of unity are derived, facilitating further analysis.
The study showcases relationships through determinants and Bell polynomials, underscoring a novel approach in mathematical expressions.
Using generating functions, recurrence relations are obtained, offering pathways for additional value types.
This work may enable deeper insights into q-multiple functions through unified expressions and their implications in number theory.

Implication

This analysis reveals explicit values of the q-multiple zeta-star function at roots of unity, suggesting potential applications to recurrence relations.

Abstract

In this paper, we show some expressions of certain q-multiple zeta-star values at roots of unity. These explicit formulas are expressed by using the determinants or Bell polynomials. Explicit formulas for other types of values can be found from recurrence relations obtained using generating functions.

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Cite This Study

Takao Komatsu (2025) studied this question.

synapsesocial.com/papers/68af454cad7bf08b1ead356e https://doi.org/10.1051/ita/2025005

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Implication

This analysis reveals explicit values of the q-multiple zeta-star function at roots of unity, suggesting potential applications to recurrence relations.

Explicit values of a q-multiple zeta-star function at roots of unity

Key Points

Implication

Abstract

Discussion

Cite This Study

Explicit values of a q-multiple zeta-star function at roots of unity

Key Points

Implication

Abstract

Discussion

Cite This Study

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