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

2025/05/14 by Takao Komatsu, Komatsu, Takao · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2505.09357

openalex publication_date 2025/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Finite and symmetric colored multiple zeta values and multiple harmonic q-series at roots of unity
• Sum of interpolated finite multiple harmonic q-series
• Some determinants involving incomplete Fubini numbers
• Some remarks on q-deformed multiple polylogarithms

Cited by

• Some explicit values of a q-multiple zeta function whose denominator power is not uniform
• Some explicit values of a q-multiple zeta-star function at roots of unity

Related

• Some explicit values of a q-multiple zeta-star function at roots of unity
• Some explicit values of a q-multiple zeta function whose denominator power is not uniform
• Special values of finite multiple harmonic q-series at roots of unity
• Stirling polynomials and multiple zeta (star) functions at non-positive integers
• q-Euler numbers and polynomials associated with multiple q-zeta functions